Minimum number of intercalates in a Latin square of order n, https://oeis.org/Axxxxxx n=1, a(1)=0 Article: Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Announcement: https://vk.com/wall162891802_2635, Eduard I. Vatutin, Jan 22 2024 Way of finding: trivial 0 n=2, a(2)=1 Announcement: https://vk.com/wall162891802_2635, Eduard I. Vatutin, Jan 22 2024 Way of finding: brute force 0 1 1 0 n=3, a(3)=0 Announcement: https://vk.com/wall162891802_2635, Eduard I. Vatutin, Jan 22 2024 Way of finding: brute force 0 1 2 1 2 0 2 0 1 n=4, a(4)=4 Announcement: https://vk.com/wall162891802_2635, Eduard I. Vatutin, Jan 22 2024 Way of finding: brute force 0 1 2 3 1 0 3 2 2 3 1 0 3 2 0 1 n=5, a(5)=0 Article (as DLS): Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Announcement (as LS): https://vk.com/wall162891802_2635, Eduard I. Vatutin, Jan 22 2024 Way of finding: brute force 0 1 2 3 4 1 4 0 2 3 2 0 3 4 1 3 2 4 1 0 4 3 1 0 2 n=6, a(6)=0 Announcement: https://vk.com/wall162891802_2635, Eduard I. Vatutin, Jan 22 2024 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 2 1 0 4 3 5 0 2 1 5 4 3 1 0 2 n=7, a(7)=0 Article (as DLS): Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Announcement (as LS): https://vk.com/wall162891802_2635, Eduard I. Vatutin, Jan 22 2024 Way of finding: brute force 0 1 2 3 4 5 6 1 3 0 4 5 6 2 2 0 6 1 3 4 5 3 4 1 5 6 2 0 4 5 3 6 2 0 1 5 6 4 2 0 1 3 6 2 5 0 1 3 4 n=8, a(8)=0 Article (as DLS): Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Announcement (as LS): https://vk.com/wall162891802_2635, Eduard I. Vatutin, Jan 22 2024 Way of finding: brute force 0 1 2 3 4 5 6 7 1 2 4 6 7 0 5 3 2 0 7 4 5 3 1 6 3 6 0 7 2 1 4 5 4 5 6 0 3 2 7 1 5 3 1 2 6 7 0 4 6 7 3 5 1 4 2 0 7 4 5 1 0 6 3 2 n=9, a(9)=0 Announcement (from DLS): https://vk.com/wall162891802_1333, Eduard I. Vatutin, Sep 10 2020 Way of finding: brute force using X-based fillings 0 2 3 4 5 6 7 8 1 5 1 4 7 8 3 2 0 6 8 7 2 5 6 1 3 4 0 6 5 8 3 7 2 0 1 4 2 6 0 8 4 7 1 5 3 4 0 7 6 1 5 8 3 2 3 4 5 1 0 8 6 2 7 1 8 6 2 3 0 4 7 5 7 3 1 0 2 4 5 6 8 n=10, a(10)=0 Announcement (from DLS): https://vk.com/wall162891802_1531, Eduard I. Vatutin, Jan 28 2021 Way of finding: random search 0 6 4 9 2 3 7 8 5 1 5 1 8 4 7 9 3 6 2 0 3 0 2 7 9 1 8 4 6 5 6 5 0 3 1 8 9 2 4 7 7 2 9 5 4 6 1 3 0 8 1 9 6 8 3 5 4 0 7 2 2 8 7 0 5 4 6 9 1 3 4 3 5 1 8 0 2 7 9 6 9 7 3 6 0 2 5 1 8 4 8 4 1 2 6 7 0 5 3 9 n=11, a(11)=0 Announcement: -, Eduard I. Vatutin, Jan 23 2021 (well known fact) Way of finding: cyclic Latin squares 0 1 2 3 4 5 6 7 8 9 10 2 3 4 5 1 7 8 9 10 6 0 3 9 5 6 7 8 2 10 4 0 1 5 6 7 8 9 10 4 0 1 2 3 6 0 8 2 10 4 5 1 7 3 9 8 2 10 4 0 1 7 3 9 5 6 10 4 0 1 2 3 9 5 6 7 8 4 5 1 7 3 9 10 6 0 8 2 1 7 3 9 5 6 0 8 2 10 4 7 8 9 10 6 0 1 2 3 4 5 9 10 6 0 8 2 3 4 5 1 7 n=12, a(12)=0 Announcement: https://vk.com/wall162891802_1618, Eduard I. Vatutin, Mar 29 2021 Way of finding: neighborhoods of centrally symmetric DLS 0 1 2 3 4 5 6 7 8 9 10 11 7 3 8 5 6 4 2 9 0 11 1 10 9 8 11 0 1 7 5 6 10 3 2 4 10 4 9 7 0 6 1 5 2 8 11 3 11 7 0 9 2 1 10 4 3 6 5 8 1 9 10 11 5 8 7 2 4 0 3 6 3 6 1 8 10 9 4 11 5 2 7 0 4 11 3 6 8 2 0 10 7 1 9 5 6 5 4 10 11 0 3 1 9 7 8 2 8 10 6 2 3 11 9 0 1 5 4 7 2 0 5 1 7 10 8 3 11 4 6 9 5 2 7 4 9 3 11 8 6 10 0 1 n=13, a(13)=0 Announcement: -, Eduard I. Vatutin, Mar 29 2021 (well known fact) Way of finding: cyclic Latin squares 0 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 0 1 4 5 6 7 8 9 10 11 12 0 1 2 3 6 7 8 9 10 11 12 0 1 2 3 4 5 8 9 10 11 12 0 1 2 3 4 5 6 7 10 11 12 0 1 2 3 4 5 6 7 8 9 12 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 0 3 4 5 6 7 8 9 10 11 12 0 1 2 5 6 7 8 9 10 11 12 0 1 2 3 4 7 8 9 10 11 12 0 1 2 3 4 5 6 9 10 11 12 0 1 2 3 4 5 6 7 8 11 12 0 1 2 3 4 5 6 7 8 9 10 n=14, a(14)=0 Announcement: https://vk.com/wall162891802_2673, Eduard I. Vatutin, Feb 27 2024 Way of finding: neighborhoods of different special types of LS and DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 9 4 5 12 7 8 13 6 3 10 11 0 2 10 3 6 8 0 13 12 1 5 7 4 9 11 3 9 6 7 0 1 12 2 11 13 8 5 4 10 4 6 5 12 1 9 2 11 10 0 13 8 7 3 5 7 0 2 11 4 10 3 9 1 12 13 8 6 6 8 13 0 2 3 9 10 4 11 1 12 5 7 7 13 12 1 9 6 3 4 5 10 11 2 0 8 8 12 1 11 10 7 4 9 6 3 2 0 13 5 9 5 8 13 12 10 11 1 3 2 0 7 6 4 10 4 7 8 13 11 1 0 2 12 5 6 3 9 11 3 4 5 7 2 0 13 12 8 6 9 10 1 12 11 10 9 6 13 8 5 0 7 4 3 1 2 13 0 11 10 3 8 5 6 7 4 9 1 2 12 n=15, a(15)=0 Announcement (from DLS): https://vk.com/wall162891802_2476, Eduard I. Vatutin, Aug 06 2023 (well known fact) Way of finding: cyclic Latin squares 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 n=16, a(16)=0 Announcement: https://vk.com/wall162891802_2679, Eduard I. Vatutin, Mar 04 2024 Way of finding: neighborhoods of special types of LS/DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 10 14 12 2 3 4 0 9 5 11 7 13 6 15 8 2 6 7 0 9 10 11 4 13 14 15 8 1 5 3 12 3 15 8 1 5 14 12 2 6 7 0 9 10 11 4 13 4 0 9 10 11 7 13 3 15 8 1 2 14 12 5 6 5 14 12 2 6 4 1 9 10 11 7 13 3 15 8 0 6 4 1 9 10 11 7 13 14 15 8 0 2 3 12 5 7 13 3 15 8 1 5 14 12 2 6 4 0 9 10 11 8 9 10 11 12 13 3 15 1 0 5 14 7 2 6 4 9 2 11 4 13 6 15 8 0 10 3 12 5 14 7 1 10 11 4 13 14 15 8 1 2 3 12 5 6 7 0 9 11 7 13 14 15 8 0 5 3 12 2 6 4 1 9 10 12 5 6 7 1 9 10 11 4 13 14 15 8 0 2 3 13 3 15 8 0 2 14 12 5 6 4 1 9 10 11 7 14 12 5 6 7 0 9 10 11 4 13 3 15 8 1 2 15 8 0 5 3 12 2 6 7 1 9 10 11 4 13 14 n=17, a(17)=0 Announcement: -, Eduard I. Vatutin, before Aug 06 2023 (well known fact) Way of finding: cyclic LS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 n=18, a(18)=0 Announcement: https://vk.com/wall162891802_2689, Eduard I. Vatutin, Mar 12 2024 Way of finding: neighborhoods of special types of LS/DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 9 4 11 8 7 3 6 10 5 0 13 14 12 16 17 15 2 9 1 5 8 10 3 6 7 11 0 4 14 12 13 17 15 16 3 11 10 13 9 2 15 17 16 1 7 14 8 5 4 0 6 12 4 0 5 12 3 6 10 8 11 2 13 9 16 15 17 14 1 7 5 4 3 6 12 9 11 10 0 8 2 13 17 16 15 7 14 1 6 7 8 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 7 3 6 10 5 0 13 14 12 16 17 15 1 2 9 4 11 8 8 5 4 0 6 12 9 11 10 13 3 2 15 17 16 1 7 14 9 6 7 11 0 4 14 12 13 17 15 16 2 3 1 5 8 10 10 8 11 2 13 3 16 15 17 14 1 7 4 0 5 12 9 6 11 10 0 8 2 13 17 16 15 7 14 1 5 4 3 6 12 9 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8 9 10 11 13 14 12 16 17 15 1 2 3 4 11 8 7 9 6 10 5 0 14 12 13 17 15 16 2 9 1 5 8 10 3 6 7 11 0 4 15 17 16 1 7 14 8 5 4 0 6 12 9 11 10 13 3 2 16 15 17 14 1 7 4 0 5 12 9 6 10 8 11 2 13 3 17 16 15 7 14 1 5 4 9 6 12 3 11 10 0 8 2 13 n=19, a(19)=0 Announcement: -, Eduard I. Vatutin, before Aug 06 2023 (well known fact) Way of finding: cyclic LS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 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 9 10 11 12 13 14 15 16 17 18 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 n=20, a(20)=0 Announcement: https://vk.com/wall162891802_2757, Eduard I. Vatutin, Apr 24 2024 Way of finding: neighborhoods of special types of LS/DLS 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 16 18 15 19 17 2 0 4 1 3 7 5 9 6 8 12 10 14 11 13 17 15 19 16 18 3 4 1 2 0 8 9 6 7 5 13 14 11 12 10 18 19 16 17 15 4 2 3 0 1 9 7 8 5 6 14 12 13 10 11 19 17 18 15 16 5 15 7 8 9 10 1 18 17 16 19 3 2 6 4 13 12 14 0 11 6 16 17 18 13 19 12 14 0 11 9 8 7 15 1 10 2 5 4 3 7 5 9 15 8 18 10 16 1 17 2 19 4 3 6 14 13 11 12 0 8 9 15 7 5 17 16 1 18 10 6 4 3 2 19 0 11 12 14 13 9 7 8 5 15 16 18 17 10 1 4 2 6 19 3 11 14 0 13 12 10 14 12 11 19 2 13 4 3 15 5 0 17 18 16 8 9 6 7 1 11 19 14 12 10 3 15 13 4 2 18 16 0 17 5 7 1 9 6 8 12 10 19 14 11 4 2 15 13 3 17 5 16 0 18 6 8 1 9 7 13 17 18 6 16 11 14 0 19 12 1 7 15 9 8 3 5 4 10 2 14 11 10 19 12 13 3 2 15 4 0 18 5 16 17 9 7 8 1 6 15 8 5 9 7 1 17 10 16 18 3 6 19 4 2 12 0 13 11 14 16 18 6 13 17 12 0 19 11 14 8 15 9 1 7 2 4 10 3 5 17 6 13 16 18 14 19 11 12 0 7 9 1 8 15 5 10 3 2 4 18 13 16 17 6 0 11 12 14 19 15 1 8 7 9 4 3 2 5 10 19 12 11 10 14 15 4 3 2 13 16 17 18 5 0 1 6 7 8 9 n=21, a(21)=0 Announcement: -, Eduard I. Vatutin, Jan 22 2024 (well known fact) Way of finding: cyclic LS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 n=22, a(22)<=9 Announcement: https://vk.com/wall162891802_2638, Eduard I. Vatutin, Jan 25 2024 Way of finding: neighborhoods of special types of DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 20 6 17 1 3 7 2 9 4 14 15 13 21 18 19 11 0 16 12 8 5 10 14 17 3 7 21 9 19 11 6 1 8 12 16 2 5 13 15 0 4 18 10 20 9 3 20 10 19 8 7 0 15 21 4 14 18 11 1 12 17 13 2 6 16 5 8 15 7 11 9 2 1 18 13 6 5 0 17 19 21 16 10 20 14 3 4 12 3 18 10 5 8 1 9 19 11 20 6 4 7 0 16 14 13 12 21 2 17 15 5 14 15 8 10 0 4 6 21 11 1 16 19 12 3 17 18 2 20 9 7 13 11 7 16 4 15 17 10 8 18 19 21 20 13 14 12 2 9 6 5 1 0 3 7 21 1 9 2 12 14 10 19 4 18 17 15 16 11 3 5 8 6 20 13 0 6 4 9 19 1 11 5 13 10 7 14 21 0 17 2 20 8 15 16 12 3 18 1 8 4 18 7 6 17 3 0 10 11 15 2 21 20 9 19 14 13 5 12 16 13 0 18 14 20 16 11 21 2 12 9 5 8 10 15 19 1 3 7 4 6 17 12 5 0 21 11 14 16 17 3 8 13 1 20 4 6 10 2 19 15 7 18 9 16 2 21 20 12 10 8 14 7 13 3 18 1 15 17 4 11 5 9 0 19 6 4 19 11 17 6 3 12 1 9 16 20 8 10 5 13 21 14 18 0 15 2 7 17 9 12 0 16 13 3 2 14 5 19 6 4 7 10 18 20 1 11 21 15 8 15 16 8 2 0 4 18 5 1 3 17 10 14 20 7 6 12 9 19 13 21 11 2 20 6 16 14 15 13 4 5 0 12 9 11 3 18 1 7 21 10 17 8 19 18 12 14 6 13 19 21 20 16 15 2 7 5 1 8 0 3 10 17 11 9 4 21 10 19 13 5 18 20 15 12 17 0 2 3 9 4 8 6 7 1 16 11 14 19 11 13 12 18 20 15 16 17 2 7 3 9 6 0 5 21 4 8 10 14 1 10 13 5 15 17 21 0 12 20 18 16 19 6 8 9 7 4 11 3 14 1 2 n=23, a(23)=0 Announcement: -, Eduard I. Vatutin, before Aug 06 2023 Way of finding: cyclic LS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 n=24, a(24)<=16 Announcement (from DLS): https://vk.com/wall162891802_2664, Eduard I. Vatutin, Feb 20 2024 Way of finding: neighborhoods of special types of DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 18 17 14 19 22 21 16 15 2 5 1 8 4 11 23 3 7 6 20 13 10 9 0 12 1 7 21 18 5 19 3 9 0 13 17 4 11 6 22 12 14 2 10 16 15 20 23 8 22 2 7 8 1 6 10 18 23 0 21 20 9 3 17 16 12 19 4 14 5 15 11 13 2 4 8 0 11 7 20 22 14 12 16 10 21 5 19 6 23 9 15 1 17 13 18 3 9 20 13 4 15 3 18 11 5 8 14 0 23 10 6 17 1 12 2 7 19 16 21 22 13 8 18 16 9 23 22 4 1 2 15 6 17 12 11 5 19 21 14 20 0 7 3 10 3 22 10 17 2 15 21 23 19 16 5 9 14 8 4 13 18 20 12 11 6 0 7 1 10 3 12 5 20 18 9 16 6 11 7 15 0 17 1 8 4 14 23 21 13 22 2 19 4 18 16 23 7 13 8 3 10 20 19 14 1 2 9 21 5 0 17 12 22 6 15 11 21 19 17 1 10 12 23 13 15 22 2 3 16 14 5 7 0 18 6 9 11 8 4 20 17 16 23 14 19 8 2 1 13 15 9 7 22 20 12 4 3 11 0 10 21 18 6 5 23 0 3 20 16 22 17 8 11 14 13 12 15 19 21 2 6 5 7 4 9 1 10 18 8 11 15 6 14 4 13 5 18 17 3 21 20 9 7 23 22 10 19 2 16 12 1 0 16 21 5 2 23 11 12 17 20 19 18 22 13 7 10 9 8 15 1 0 3 4 14 6 12 10 1 22 0 9 19 14 16 3 6 5 8 23 2 18 20 4 21 17 7 11 13 15 20 12 0 15 21 16 14 6 4 7 22 19 10 1 18 11 13 23 5 3 2 17 8 9 6 5 22 9 3 0 11 10 12 4 20 18 7 21 15 19 2 1 13 8 14 23 16 17 19 23 20 11 8 10 1 21 7 18 0 17 2 15 13 22 9 3 16 6 12 14 5 4 15 13 11 12 17 14 4 20 22 1 23 16 6 0 3 10 21 8 9 5 18 2 19 7 14 9 19 13 12 1 7 2 17 6 8 23 5 18 16 0 11 22 3 15 4 10 20 21 5 14 4 21 6 2 15 0 3 10 12 13 18 22 8 20 17 7 11 23 1 19 9 16 11 15 6 7 18 17 0 19 9 21 4 1 3 16 20 14 10 13 8 22 23 5 12 2 7 6 9 10 13 20 5 12 21 23 11 2 19 4 0 1 15 16 22 18 8 3 17 14 n=25, a(25)=0 Announcement: -, Eduard I. Vatutin, Dec 23 2023 Way of finding: composite squares method 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 3 0 1 9 7 8 5 6 14 12 13 10 11 19 17 18 15 16 24 22 23 20 21 3 4 1 2 0 8 9 6 7 5 13 14 11 12 10 18 19 16 17 15 23 24 21 22 20 1 3 0 4 2 6 8 5 9 7 11 13 10 14 12 16 18 15 19 17 21 23 20 24 22 2 0 4 1 3 7 5 9 6 8 12 10 14 11 13 17 15 19 16 18 22 20 24 21 23 20 21 22 23 24 10 11 12 13 14 15 16 17 18 19 0 1 2 3 4 5 6 7 8 9 24 22 23 20 21 14 12 13 10 11 19 17 18 15 16 4 2 3 0 1 9 7 8 5 6 23 24 21 22 20 13 14 11 12 10 18 19 16 17 15 3 4 1 2 0 8 9 6 7 5 21 23 20 24 22 11 13 10 14 12 16 18 15 19 17 1 3 0 4 2 6 8 5 9 7 22 20 24 21 23 12 10 14 11 13 17 15 19 16 18 2 0 4 1 3 7 5 9 6 8 15 16 17 18 19 20 21 22 23 24 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 19 17 18 15 16 24 22 23 20 21 9 7 8 5 6 14 12 13 10 11 4 2 3 0 1 18 19 16 17 15 23 24 21 22 20 8 9 6 7 5 13 14 11 12 10 3 4 1 2 0 16 18 15 19 17 21 23 20 24 22 6 8 5 9 7 11 13 10 14 12 1 3 0 4 2 17 15 19 16 18 22 20 24 21 23 7 5 9 6 8 12 10 14 11 13 2 0 4 1 3 5 6 7 8 9 15 16 17 18 19 0 1 2 3 4 20 21 22 23 24 10 11 12 13 14 9 7 8 5 6 19 17 18 15 16 4 2 3 0 1 24 22 23 20 21 14 12 13 10 11 8 9 6 7 5 18 19 16 17 15 3 4 1 2 0 23 24 21 22 20 13 14 11 12 10 6 8 5 9 7 16 18 15 19 17 1 3 0 4 2 21 23 20 24 22 11 13 10 14 12 7 5 9 6 8 17 15 19 16 18 2 0 4 1 3 22 20 24 21 23 12 10 14 11 13 10 11 12 13 14 0 1 2 3 4 20 21 22 23 24 5 6 7 8 9 15 16 17 18 19 14 12 13 10 11 4 2 3 0 1 24 22 23 20 21 9 7 8 5 6 19 17 18 15 16 13 14 11 12 10 3 4 1 2 0 23 24 21 22 20 8 9 6 7 5 18 19 16 17 15 11 13 10 14 12 1 3 0 4 2 21 23 20 24 22 6 8 5 9 7 16 18 15 19 17 12 10 14 11 13 2 0 4 1 3 22 20 24 21 23 7 5 9 6 8 17 15 19 16 18 Apr 24 2024