Maximum number of intercalates in a Latin square of order n, https://oeis.org/A092237 n=1, a(1)=0 Announcement: -, Richard Bean, Feb 17 2004 Way of finding: trivial 0 n=2, a(2)=1 Announcement: -, Richard Bean, Feb 17 2004 Way of finding: trivial 0 1 1 0 n=3, a(3)=0 Announcement: -, Richard Bean, Feb 17 2004 Way of finding: trivial 0 1 2 1 2 0 2 0 1 n=4, a(4)=12 Announcement: -, Richard Bean, Feb 17 2004 Way of finding: brute force 0 1 2 3 1 0 3 2 2 3 0 1 3 2 1 0 n=5, a(5)=4 Announcement: -, Richard Bean, Feb 17 2004 Way of finding: brute force 0 1 2 3 4 1 4 3 2 0 2 3 4 0 1 3 0 1 4 2 4 2 0 1 3 n=6, a(6)=27 Announcement: -, Richard Bean, Feb 17 2004 Way of finding: brute force 0 1 2 3 4 5 1 2 0 4 5 3 2 0 1 5 3 4 3 5 4 0 2 1 4 3 5 1 0 2 5 4 3 2 1 0 n=7, a(7)=42 Announcement: -, Richard Bean, Feb 17 2004 Way of finding: brute force 0 1 2 3 4 5 6 1 0 3 2 6 4 5 2 6 4 5 0 3 1 3 2 1 0 5 6 4 4 5 0 6 2 1 3 5 4 6 1 3 0 2 6 3 5 4 1 2 0 n=8, a(8)=112 Announcement: -, Richard Bean, Feb 17 2004 Way of finding: brute force 0 1 2 3 4 5 6 7 1 0 4 6 2 7 3 5 2 4 0 5 1 3 7 6 3 6 5 0 7 2 1 4 4 2 1 7 0 6 5 3 5 7 3 2 6 0 4 1 6 3 7 1 5 4 0 2 7 5 6 4 3 1 2 0 n=9, a(9)=72 Announcement: -, Richard Bean, Feb 17 2004 Way of finding: brute force 0 1 2 3 4 5 6 7 8 1 0 5 7 2 6 8 3 4 2 4 0 8 1 3 5 6 7 3 2 4 0 6 8 7 1 5 4 5 1 6 0 7 3 8 2 5 7 6 1 8 0 2 4 3 6 8 3 4 7 2 0 5 1 7 3 8 2 5 4 1 0 6 8 6 7 5 3 1 4 2 0 n=10, a(10)>=125 Announcement 1 (lower bound only): -, Richard Bean, Feb 17 2004 Announcement 2 (proving LS): https://vk.com/wall162891802_2644, Eduard I. Vatutin, Feb 01 2024 Way of finding: composite squares 2x5, pine LS 0 1 2 3 4 5 6 7 8 9 1 2 3 4 0 9 5 6 7 8 2 3 4 0 1 8 9 5 6 7 3 4 0 1 2 7 8 9 5 6 4 0 1 2 3 6 7 8 9 5 5 6 7 8 9 0 1 2 3 4 6 7 8 9 5 4 0 1 2 3 7 8 9 5 6 3 4 0 1 2 8 9 5 6 7 2 3 4 0 1 9 5 6 7 8 1 2 3 4 0 n=11, a(11)>=172 Announcement: Critical sets in Latin squares and associated structures, Ph.D. Thesis, The University of Queensland, 2001, Richard Bean Way of finding: ? 0 1 2 3 4 5 6 7 8 9 10 1 9 0 5 3 4 8 6 7 10 2 2 10 9 8 7 6 5 4 3 0 1 3 4 5 0 1 8 9 10 2 6 7 4 5 3 7 0 1 10 2 9 8 6 5 3 4 1 6 0 2 9 10 7 8 6 7 8 9 10 2 0 1 5 3 4 7 8 6 10 2 9 4 0 1 5 3 8 6 7 2 9 10 1 3 0 4 5 9 2 10 6 8 7 3 5 4 1 0 10 0 1 4 5 3 7 8 6 2 9 n=12, a(12)>=324 Announcement 1 (lower bound only): -, Richard Bean, Feb 17 2004 Announcement 2 (proving LS): https://vk.com/wall162891802_2667, Eduard I. Vatutin, Feb 23 2024 Way of finding: neighborhoods of different special types of LS/DLS 0 1 2 3 4 5 6 7 8 9 10 11 1 2 0 5 3 4 7 8 6 10 11 9 2 0 1 4 5 3 8 6 7 11 9 10 3 4 5 0 1 2 10 9 11 7 6 8 4 5 3 2 0 1 11 10 9 8 7 6 5 3 4 1 2 0 9 11 10 6 8 7 6 8 7 10 11 9 0 2 1 5 3 4 7 6 8 9 10 11 1 0 2 3 4 5 8 7 6 11 9 10 2 1 0 4 5 3 9 11 10 7 8 6 5 3 4 0 2 1 10 9 11 6 7 8 3 4 5 1 0 2 11 10 9 8 6 7 4 5 3 2 1 0 n=13, a(13)>=208 Announcement: https://vk.com/wall162891802_2641, Eduard I. Vatutin, Jan 28 2024 Way of finding: neighborhoods of different special types of DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 1 2 0 4 5 3 7 6 11 8 12 10 9 9 12 10 7 8 6 5 3 4 11 2 0 1 10 6 12 9 7 8 4 11 5 3 0 1 2 4 0 1 5 3 2 8 10 9 7 6 12 11 7 10 6 8 9 12 1 0 3 4 11 2 5 12 9 3 2 10 0 11 4 7 5 1 6 8 2 5 11 0 1 4 3 8 6 12 9 7 10 11 8 9 10 6 7 12 5 1 2 3 4 0 5 3 4 1 2 11 0 12 10 6 8 9 7 3 4 5 11 0 1 2 9 12 10 7 8 6 6 7 8 12 11 9 10 1 2 0 4 5 3 8 11 7 6 12 10 9 2 0 1 5 3 4 n=14, a(14)>=391 Announcement: https://vk.com/wall162891802_2673, Eduard I. Vatutin, Feb 27 2024 Way of finding: neighborhoods of different special types of LS/DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 0 4 3 6 5 8 7 10 9 13 11 12 2 0 1 6 5 4 3 10 9 8 7 12 13 11 3 5 4 7 0 1 2 11 12 13 6 9 8 10 4 6 3 0 8 2 1 12 11 5 13 10 7 9 5 3 6 1 2 0 4 9 13 11 12 7 10 8 6 4 5 2 1 3 0 13 10 12 11 8 9 7 7 9 8 11 12 13 10 3 0 1 2 5 4 6 8 10 7 12 11 9 13 0 4 2 1 6 3 5 9 7 10 5 13 11 12 1 2 0 8 3 6 4 10 8 9 13 6 12 11 2 1 7 0 4 5 3 11 12 13 10 9 8 7 6 5 4 3 0 1 2 12 13 11 8 7 10 9 4 3 6 5 2 0 1 13 11 12 9 10 7 8 5 6 3 4 1 2 0 n=15, a(15)>=630 Announcement: https://vk.com/wall162891802_2675, Eduard I. Vatutin, Feb 28 2024 Way of finding: neighborhoods of different special types of LS/DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 0 6 7 12 2 5 3 9 8 13 14 4 10 11 2 6 0 1 14 7 3 5 10 13 8 12 11 9 4 3 7 5 0 9 6 2 1 12 4 11 10 8 14 13 4 12 14 9 0 10 13 8 7 3 5 6 1 11 2 5 3 7 6 10 0 1 2 14 11 4 9 13 12 8 6 2 1 5 11 3 7 0 13 10 9 4 14 8 12 7 5 3 2 13 1 0 6 11 14 12 8 10 4 9 8 9 10 12 7 14 11 4 0 1 2 13 3 6 5 9 8 13 4 3 11 14 12 1 0 6 5 7 2 10 10 13 8 11 5 4 12 14 2 6 0 3 9 1 7 11 14 12 10 6 9 8 13 4 5 3 0 2 7 1 12 4 11 8 1 13 10 9 3 7 14 2 0 5 6 13 10 9 14 8 12 4 11 6 2 1 7 5 0 3 14 11 4 13 2 8 9 10 5 12 7 1 6 3 0 n=16, a(16)>=960 Announcement: https://vk.com/wall162891802_2583, Eduard I. Vatutin, Dec 23 2023 Way of finding: composite squares method 4x4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 3 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14 2 3 0 1 6 7 4 5 10 11 8 9 14 15 12 13 12 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 13 12 15 14 9 8 11 10 5 4 7 6 1 0 3 2 14 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1 4 5 6 7 0 1 2 3 12 13 14 15 8 9 10 11 7 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8 5 4 7 6 1 0 3 2 13 12 15 14 9 8 11 10 6 7 4 5 2 3 0 1 14 15 12 13 10 11 8 9 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 11 10 9 8 15 14 13 12 3 2 1 0 7 6 5 4 9 8 11 10 13 12 15 14 1 0 3 2 5 4 7 6 10 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5 n=17, a(17)>=736 Announcement: https://vk.com/wall162891802_2594, Eduard I. Vatutin, Dec 31 2023 Way of finding: from DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 11 15 16 12 8 14 0 5 4 13 6 7 10 9 1 2 3 8 10 3 11 9 13 2 15 0 14 1 5 4 7 6 16 12 9 13 7 8 10 6 1 12 3 15 2 16 0 14 4 5 11 10 6 1 4 13 7 5 16 9 8 3 12 11 15 2 14 0 15 7 5 16 14 1 4 0 11 6 13 8 9 10 3 12 2 12 3 4 0 11 2 16 14 15 10 5 1 13 6 7 8 9 6 9 8 14 15 10 12 11 2 3 7 0 16 1 5 4 13 1 5 6 13 2 3 7 9 10 12 8 4 15 11 16 0 14 2 16 0 5 1 12 8 4 6 7 9 13 14 3 10 11 15 3 12 11 15 0 16 9 13 14 5 4 6 1 2 8 7 10 7 8 9 10 3 15 11 6 1 2 0 14 5 16 12 13 4 14 4 13 6 7 8 3 10 5 16 12 15 2 0 11 9 1 16 2 14 1 5 4 13 8 7 0 11 9 3 12 15 10 6 5 11 12 2 16 0 14 1 13 4 15 10 6 8 9 3 7 4 0 10 9 12 11 15 2 16 1 14 3 7 5 13 6 8 13 14 15 7 6 9 10 3 12 11 16 2 8 4 0 1 5 n=18, a(18)>=729 Announcement: https://vk.com/wall162891802_2644, Eduard I. Vatutin, Feb 01 2024 Way of finding: composite squares method 2x9, pine LS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 0 17 9 10 11 12 13 14 15 16 2 3 4 5 6 7 8 0 1 16 17 9 10 11 12 13 14 15 3 4 5 6 7 8 0 1 2 15 16 17 9 10 11 12 13 14 4 5 6 7 8 0 1 2 3 14 15 16 17 9 10 11 12 13 5 6 7 8 0 1 2 3 4 13 14 15 16 17 9 10 11 12 6 7 8 0 1 2 3 4 5 12 13 14 15 16 17 9 10 11 7 8 0 1 2 3 4 5 6 11 12 13 14 15 16 17 9 10 8 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 9 8 0 1 2 3 4 5 6 7 11 12 13 14 15 16 17 9 10 7 8 0 1 2 3 4 5 6 12 13 14 15 16 17 9 10 11 6 7 8 0 1 2 3 4 5 13 14 15 16 17 9 10 11 12 5 6 7 8 0 1 2 3 4 14 15 16 17 9 10 11 12 13 4 5 6 7 8 0 1 2 3 15 16 17 9 10 11 12 13 14 3 4 5 6 7 8 0 1 2 16 17 9 10 11 12 13 14 15 2 3 4 5 6 7 8 0 1 17 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 0 n=19, a(19)>=472 Announcement: https://vk.com/wall162891802_2742, Eduard I. Vatutin, Apr 11 2024 Way of finding: neighborhoods of different special types of LS/DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 3 7 5 4 0 8 17 12 9 10 18 14 13 11 15 16 6 2 0 10 12 11 9 15 13 1 14 4 5 3 17 7 6 8 18 16 3 17 12 0 10 11 16 14 13 6 5 4 2 7 8 18 1 9 15 4 10 0 15 9 12 13 11 16 17 2 7 5 6 1 3 18 8 14 5 16 14 11 12 0 9 15 10 8 1 3 17 18 6 7 4 2 13 6 11 15 16 13 14 18 10 9 0 17 8 1 4 5 2 3 7 12 7 12 9 13 0 10 14 16 15 11 3 2 4 8 18 5 17 6 1 8 14 13 9 15 2 11 12 0 16 18 6 7 1 3 17 5 4 10 9 18 8 4 6 7 1 3 2 5 16 15 13 11 12 14 10 0 17 10 4 17 5 1 16 7 6 18 3 0 12 11 2 15 13 9 14 8 11 5 4 1 2 3 17 18 6 10 12 0 9 15 16 8 14 13 7 12 9 7 10 3 18 5 2 14 1 8 13 0 16 17 4 6 15 11 13 7 6 2 8 1 4 17 3 18 15 9 14 0 10 16 12 11 5 14 15 5 17 18 6 8 1 7 2 11 16 10 12 0 9 13 3 4 15 6 1 18 17 8 2 4 5 7 13 14 16 10 9 0 11 12 3 16 8 18 6 7 17 3 5 4 13 14 1 15 9 11 12 0 10 2 17 13 11 14 16 15 10 0 12 4 6 18 8 3 2 1 7 5 9 18 3 16 8 14 13 12 9 11 15 7 17 6 5 4 10 2 1 0 n=20, a(20)>=1500 Announcement: https://vk.com/wall162891802_2757, Eduard I. Vatutin, Apr 24 2024 Way of finding: neighborhoods of special types of LS/DLS, noncanonical composite LS 4x5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 3 0 4 2 6 8 5 9 7 11 13 10 14 12 17 15 19 16 18 2 0 4 1 3 7 5 9 6 8 12 10 14 11 13 16 18 15 19 17 3 4 1 2 0 8 9 6 7 5 13 14 11 12 10 19 17 18 15 16 4 2 3 0 1 9 7 8 5 6 14 12 13 10 11 18 19 16 17 15 5 7 6 9 8 0 2 1 4 3 17 15 19 16 18 11 13 10 14 12 6 5 8 7 9 1 0 3 2 4 15 16 17 18 19 10 11 12 13 14 7 9 5 8 6 2 4 0 3 1 19 17 18 15 16 13 14 11 12 10 8 6 9 5 7 3 1 4 0 2 16 18 15 19 17 12 10 14 11 13 9 8 7 6 5 4 3 2 1 0 18 19 16 17 15 14 12 13 10 11 10 12 11 14 13 17 15 19 16 18 0 2 1 4 3 6 8 5 9 7 11 10 13 12 14 15 16 17 18 19 1 0 3 2 4 5 6 7 8 9 12 14 10 13 11 19 17 18 15 16 2 4 0 3 1 8 9 6 7 5 13 11 14 10 12 16 18 15 19 17 3 1 4 0 2 7 5 9 6 8 14 13 12 11 10 18 19 16 17 15 4 3 2 1 0 9 7 8 5 6 15 16 17 18 19 11 10 13 12 14 6 5 8 7 9 0 1 2 3 4 16 18 15 19 17 13 11 14 10 12 8 6 9 5 7 2 0 4 1 3 17 15 19 16 18 10 12 11 14 13 5 7 6 9 8 1 3 0 4 2 18 19 16 17 15 14 13 12 11 10 9 8 7 6 5 4 2 3 0 1 19 17 18 15 16 12 14 10 13 11 7 9 5 8 6 3 4 1 2 0 n=21, a(21)>=408 Announcement: https://vk.com/wall162891802_2633, Eduard I. Vatutin, Jan 22 2024 Way of finding: from DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 8 6 1 9 2 19 7 3 4 5 20 15 16 17 13 10 18 11 0 14 12 1 5 3 4 8 0 9 19 6 2 13 18 14 10 11 20 12 16 17 15 7 3 0 7 2 9 6 5 1 19 4 12 16 10 8 15 14 11 18 13 20 17 4 8 5 1 19 7 2 9 0 3 14 17 20 11 18 13 10 6 15 12 16 2 3 19 0 6 9 1 5 7 8 16 12 13 15 4 11 14 20 10 17 18 7 4 9 19 5 1 8 0 2 6 17 14 18 20 12 3 15 10 11 16 13 9 7 6 8 1 2 19 4 3 0 15 20 17 16 10 18 5 12 14 13 11 19 9 4 7 0 8 3 6 5 1 18 2 15 14 17 12 20 13 16 11 10 6 19 8 5 3 4 0 2 1 7 11 13 9 18 20 16 17 15 12 10 14 13 18 20 14 15 17 16 12 11 10 1 5 4 19 9 2 8 0 6 7 3 12 14 15 11 18 20 13 17 16 19 4 10 1 3 7 0 2 9 5 6 8 18 20 13 12 17 16 15 10 9 14 19 6 11 1 5 4 3 8 7 0 2 16 11 17 13 10 14 20 8 18 15 5 1 2 12 0 6 19 7 3 9 4 20 17 14 18 11 15 4 13 10 12 6 8 19 7 16 5 9 2 1 3 0 15 16 12 10 13 3 11 18 14 20 9 0 6 2 1 17 7 19 8 4 5 14 12 18 20 7 11 10 16 15 17 0 3 5 4 19 9 13 1 2 8 6 11 10 16 6 12 13 17 15 20 18 8 19 0 5 3 7 1 14 4 2 9 10 15 0 17 16 18 14 11 12 13 2 7 8 9 6 1 4 3 20 5 19 17 2 11 15 14 10 12 20 13 16 3 4 7 0 8 19 6 5 9 18 1 5 13 10 16 20 12 18 14 17 11 7 9 3 6 2 8 0 4 19 1 15 n=22, a(22)>=1497 Announcement: -, Eduard I. Vatutin, Jan 23 2024 Way of finding: composite squares method 2x11 9 10 2 3 4 5 6 7 8 0 1 20 21 13 14 15 16 17 18 19 11 12 1 9 10 4 5 3 7 8 6 2 0 12 20 21 15 16 14 18 19 17 13 11 10 0 9 5 3 4 8 6 7 1 2 21 11 20 16 14 15 19 17 18 12 13 3 4 5 9 10 8 0 1 2 6 7 14 15 16 20 21 19 11 12 13 17 18 4 5 3 7 9 10 1 2 0 8 6 15 16 14 18 20 21 12 13 11 19 17 5 3 4 10 6 9 2 0 1 7 8 16 14 15 21 17 20 13 11 12 18 19 6 7 8 0 1 2 9 10 5 3 4 17 18 19 11 12 13 20 21 16 14 15 7 8 6 1 2 0 4 9 10 5 3 18 19 17 12 13 11 15 20 21 16 14 8 6 7 2 0 1 10 3 9 4 5 19 17 18 13 11 12 21 14 20 15 16 0 2 1 6 8 7 3 5 4 10 9 11 13 12 17 19 18 14 16 15 21 20 2 1 0 8 7 6 5 4 3 9 10 13 12 11 19 18 17 16 15 14 20 21 20 21 13 14 15 16 17 18 19 11 12 9 10 2 3 4 5 6 7 8 0 1 12 20 21 15 16 14 18 19 17 13 11 1 9 10 4 5 3 7 8 6 2 0 21 11 20 16 14 15 19 17 18 12 13 10 0 9 5 3 4 8 6 7 1 2 14 15 16 20 21 19 11 12 13 17 18 3 4 5 9 10 8 0 1 2 6 7 15 16 14 18 20 21 12 13 11 19 17 4 5 3 7 9 10 1 2 0 8 6 16 14 15 21 17 20 13 11 12 18 19 5 3 4 10 6 9 2 0 1 7 8 17 18 19 11 12 13 20 21 16 14 15 6 7 8 0 1 2 9 10 5 3 4 18 19 17 12 13 11 15 20 21 16 14 7 8 6 1 2 0 4 9 10 5 3 19 17 18 13 11 12 21 14 20 15 16 8 6 7 2 0 1 10 3 9 4 5 11 13 12 17 19 18 14 16 15 21 20 0 2 1 6 8 7 3 5 4 10 9 13 12 11 19 18 17 16 15 14 20 21 2 1 0 8 7 6 5 4 3 9 10 n=23 ? n=24, a(24)>=1872 Announcement: https://vk.com/wall162891802_2644, Eduard I. Vatutin, Feb 01 2024 Way of finding: composite squares method 2x12, pine LS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 2 3 4 5 6 7 8 9 10 11 0 23 12 13 14 15 16 17 18 19 20 21 22 2 3 4 5 6 7 8 9 10 11 0 1 22 23 12 13 14 15 16 17 18 19 20 21 3 4 5 6 7 8 9 10 11 0 1 2 21 22 23 12 13 14 15 16 17 18 19 20 4 5 6 7 8 9 10 11 0 1 2 3 20 21 22 23 12 13 14 15 16 17 18 19 5 6 7 8 9 10 11 0 1 2 3 4 19 20 21 22 23 12 13 14 15 16 17 18 6 7 8 9 10 11 0 1 2 3 4 5 18 19 20 21 22 23 12 13 14 15 16 17 7 8 9 10 11 0 1 2 3 4 5 6 17 18 19 20 21 22 23 12 13 14 15 16 8 9 10 11 0 1 2 3 4 5 6 7 16 17 18 19 20 21 22 23 12 13 14 15 9 10 11 0 1 2 3 4 5 6 7 8 15 16 17 18 19 20 21 22 23 12 13 14 10 11 0 1 2 3 4 5 6 7 8 9 14 15 16 17 18 19 20 21 22 23 12 13 11 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 19 20 21 22 23 12 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 12 11 0 1 2 3 4 5 6 7 8 9 10 14 15 16 17 18 19 20 21 22 23 12 13 10 11 0 1 2 3 4 5 6 7 8 9 15 16 17 18 19 20 21 22 23 12 13 14 9 10 11 0 1 2 3 4 5 6 7 8 16 17 18 19 20 21 22 23 12 13 14 15 8 9 10 11 0 1 2 3 4 5 6 7 17 18 19 20 21 22 23 12 13 14 15 16 7 8 9 10 11 0 1 2 3 4 5 6 18 19 20 21 22 23 12 13 14 15 16 17 6 7 8 9 10 11 0 1 2 3 4 5 19 20 21 22 23 12 13 14 15 16 17 18 5 6 7 8 9 10 11 0 1 2 3 4 20 21 22 23 12 13 14 15 16 17 18 19 4 5 6 7 8 9 10 11 0 1 2 3 21 22 23 12 13 14 15 16 17 18 19 20 3 4 5 6 7 8 9 10 11 0 1 2 22 23 12 13 14 15 16 17 18 19 20 21 2 3 4 5 6 7 8 9 10 11 0 1 23 12 13 14 15 16 17 18 19 20 21 22 1 2 3 4 5 6 7 8 9 10 11 0 n=25, a(25)>=264 Announcement: -, Eduard I. Vatutin, Dec 23 2023 Way of finding: composite squares method 5x5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 4 2 0 1 3 9 7 5 6 8 14 12 10 11 13 19 17 15 16 18 24 22 20 21 23 1 4 3 2 0 6 9 8 7 5 11 14 13 12 10 16 19 18 17 15 21 24 23 22 20 3 0 1 4 2 8 5 6 9 7 13 10 11 14 12 18 15 16 19 17 23 20 21 24 22 2 3 4 0 1 7 8 9 5 6 12 13 14 10 11 17 18 19 15 16 22 23 24 20 21 20 21 22 23 24 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 15 16 17 18 19 24 22 20 21 23 14 12 10 11 13 4 2 0 1 3 9 7 5 6 8 19 17 15 16 18 21 24 23 22 20 11 14 13 12 10 1 4 3 2 0 6 9 8 7 5 16 19 18 17 15 23 20 21 24 22 13 10 11 14 12 3 0 1 4 2 8 5 6 9 7 18 15 16 19 17 22 23 24 20 21 12 13 14 10 11 2 3 4 0 1 7 8 9 5 6 17 18 19 15 16 5 6 7 8 9 20 21 22 23 24 15 16 17 18 19 10 11 12 13 14 0 1 2 3 4 9 7 5 6 8 24 22 20 21 23 19 17 15 16 18 14 12 10 11 13 4 2 0 1 3 6 9 8 7 5 21 24 23 22 20 16 19 18 17 15 11 14 13 12 10 1 4 3 2 0 8 5 6 9 7 23 20 21 24 22 18 15 16 19 17 13 10 11 14 12 3 0 1 4 2 7 8 9 5 6 22 23 24 20 21 17 18 19 15 16 12 13 14 10 11 2 3 4 0 1 15 16 17 18 19 0 1 2 3 4 5 6 7 8 9 20 21 22 23 24 10 11 12 13 14 19 17 15 16 18 4 2 0 1 3 9 7 5 6 8 24 22 20 21 23 14 12 10 11 13 16 19 18 17 15 1 4 3 2 0 6 9 8 7 5 21 24 23 22 20 11 14 13 12 10 18 15 16 19 17 3 0 1 4 2 8 5 6 9 7 23 20 21 24 22 13 10 11 14 12 17 18 19 15 16 2 3 4 0 1 7 8 9 5 6 22 23 24 20 21 12 13 14 10 11 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 14 12 10 11 13 19 17 15 16 18 24 22 20 21 23 4 2 0 1 3 9 7 5 6 8 11 14 13 12 10 16 19 18 17 15 21 24 23 22 20 1 4 3 2 0 6 9 8 7 5 13 10 11 14 12 18 15 16 19 17 23 20 21 24 22 3 0 1 4 2 8 5 6 9 7 12 13 14 10 11 17 18 19 15 16 22 23 24 20 21 2 3 4 0 1 7 8 9 5 6 n=26, a(26)>=2197 Announcement: https://vk.com/wall162891802_2644, Eduard I. Vatutin, Feb 01 2024 Way of finding: composite squares method 2x12, pine LS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 0 25 13 14 15 16 17 18 19 20 21 22 23 24 2 3 4 5 6 7 8 9 10 11 12 0 1 24 25 13 14 15 16 17 18 19 20 21 22 23 3 4 5 6 7 8 9 10 11 12 0 1 2 23 24 25 13 14 15 16 17 18 19 20 21 22 4 5 6 7 8 9 10 11 12 0 1 2 3 22 23 24 25 13 14 15 16 17 18 19 20 21 5 6 7 8 9 10 11 12 0 1 2 3 4 21 22 23 24 25 13 14 15 16 17 18 19 20 6 7 8 9 10 11 12 0 1 2 3 4 5 20 21 22 23 24 25 13 14 15 16 17 18 19 7 8 9 10 11 12 0 1 2 3 4 5 6 19 20 21 22 23 24 25 13 14 15 16 17 18 8 9 10 11 12 0 1 2 3 4 5 6 7 18 19 20 21 22 23 24 25 13 14 15 16 17 9 10 11 12 0 1 2 3 4 5 6 7 8 17 18 19 20 21 22 23 24 25 13 14 15 16 10 11 12 0 1 2 3 4 5 6 7 8 9 16 17 18 19 20 21 22 23 24 25 13 14 15 11 12 0 1 2 3 4 5 6 7 8 9 10 15 16 17 18 19 20 21 22 23 24 25 13 14 12 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19 20 21 22 23 24 25 13 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 13 12 0 1 2 3 4 5 6 7 8 9 10 11 15 16 17 18 19 20 21 22 23 24 25 13 14 11 12 0 1 2 3 4 5 6 7 8 9 10 16 17 18 19 20 21 22 23 24 25 13 14 15 10 11 12 0 1 2 3 4 5 6 7 8 9 17 18 19 20 21 22 23 24 25 13 14 15 16 9 10 11 12 0 1 2 3 4 5 6 7 8 18 19 20 21 22 23 24 25 13 14 15 16 17 8 9 10 11 12 0 1 2 3 4 5 6 7 19 20 21 22 23 24 25 13 14 15 16 17 18 7 8 9 10 11 12 0 1 2 3 4 5 6 20 21 22 23 24 25 13 14 15 16 17 18 19 6 7 8 9 10 11 12 0 1 2 3 4 5 21 22 23 24 25 13 14 15 16 17 18 19 20 5 6 7 8 9 10 11 12 0 1 2 3 4 22 23 24 25 13 14 15 16 17 18 19 20 21 4 5 6 7 8 9 10 11 12 0 1 2 3 23 24 25 13 14 15 16 17 18 19 20 21 22 3 4 5 6 7 8 9 10 11 12 0 1 2 24 25 13 14 15 16 17 18 19 20 21 22 23 2 3 4 5 6 7 8 9 10 11 12 0 1 25 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8 9 10 11 12 0 n=27 ? n=28, a(28)>=2940 Announcement: https://vk.com/wall162891802_2644, Eduard I. Vatutin, Feb 01 2024 Way of finding: composite squares method 2x12, pine LS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1 2 3 4 5 6 7 8 9 10 11 12 13 0 27 14 15 16 17 18 19 20 21 22 23 24 25 26 2 3 4 5 6 7 8 9 10 11 12 13 0 1 26 27 14 15 16 17 18 19 20 21 22 23 24 25 3 4 5 6 7 8 9 10 11 12 13 0 1 2 25 26 27 14 15 16 17 18 19 20 21 22 23 24 4 5 6 7 8 9 10 11 12 13 0 1 2 3 24 25 26 27 14 15 16 17 18 19 20 21 22 23 5 6 7 8 9 10 11 12 13 0 1 2 3 4 23 24 25 26 27 14 15 16 17 18 19 20 21 22 6 7 8 9 10 11 12 13 0 1 2 3 4 5 22 23 24 25 26 27 14 15 16 17 18 19 20 21 7 8 9 10 11 12 13 0 1 2 3 4 5 6 21 22 23 24 25 26 27 14 15 16 17 18 19 20 8 9 10 11 12 13 0 1 2 3 4 5 6 7 20 21 22 23 24 25 26 27 14 15 16 17 18 19 9 10 11 12 13 0 1 2 3 4 5 6 7 8 19 20 21 22 23 24 25 26 27 14 15 16 17 18 10 11 12 13 0 1 2 3 4 5 6 7 8 9 18 19 20 21 22 23 24 25 26 27 14 15 16 17 11 12 13 0 1 2 3 4 5 6 7 8 9 10 17 18 19 20 21 22 23 24 25 26 27 14 15 16 12 13 0 1 2 3 4 5 6 7 8 9 10 11 16 17 18 19 20 21 22 23 24 25 26 27 14 15 13 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 18 19 20 21 22 23 24 25 26 27 14 14 15 16 17 18 19 20 21 22 23 24 25 26 27 0 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19 20 21 22 23 24 25 26 27 14 13 0 1 2 3 4 5 6 7 8 9 10 11 12 16 17 18 19 20 21 22 23 24 25 26 27 14 15 12 13 0 1 2 3 4 5 6 7 8 9 10 11 17 18 19 20 21 22 23 24 25 26 27 14 15 16 11 12 13 0 1 2 3 4 5 6 7 8 9 10 18 19 20 21 22 23 24 25 26 27 14 15 16 17 10 11 12 13 0 1 2 3 4 5 6 7 8 9 19 20 21 22 23 24 25 26 27 14 15 16 17 18 9 10 11 12 13 0 1 2 3 4 5 6 7 8 20 21 22 23 24 25 26 27 14 15 16 17 18 19 8 9 10 11 12 13 0 1 2 3 4 5 6 7 21 22 23 24 25 26 27 14 15 16 17 18 19 20 7 8 9 10 11 12 13 0 1 2 3 4 5 6 22 23 24 25 26 27 14 15 16 17 18 19 20 21 6 7 8 9 10 11 12 13 0 1 2 3 4 5 23 24 25 26 27 14 15 16 17 18 19 20 21 22 5 6 7 8 9 10 11 12 13 0 1 2 3 4 24 25 26 27 14 15 16 17 18 19 20 21 22 23 4 5 6 7 8 9 10 11 12 13 0 1 2 3 25 26 27 14 15 16 17 18 19 20 21 22 23 24 3 4 5 6 7 8 9 10 11 12 13 0 1 2 26 27 14 15 16 17 18 19 20 21 22 23 24 25 2 3 4 5 6 7 8 9 10 11 12 13 0 1 27 14 15 16 17 18 19 20 21 22 23 24 25 26 1 2 3 4 5 6 7 8 9 10 11 12 13 0 Apr 24 2024