Maximum number of intercalates in a diagonal Latin square of order n, https://oeis.org/A307164 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 Way of finding: trivial 0 n=2, a(2)=0 - n=3, a(3)=0 - n=4, a(4)=12 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 Way of finding: brute force 0 1 2 3 3 2 1 0 1 0 3 2 2 3 0 1 n=5, a(5)=4 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 Way of finding: brute force 0 1 2 3 4 4 2 0 1 3 1 4 3 2 0 3 0 1 4 2 2 3 4 0 1 n=6, a(6)=9 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 Way of finding: brute force 0 1 2 3 4 5 4 2 5 0 3 1 3 5 1 2 0 4 5 3 0 4 1 2 2 4 3 1 5 0 1 0 4 5 2 3 n=7, a(7)=30 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 Way of finding: brute force 0 1 2 3 4 5 6 4 2 6 5 0 1 3 3 6 1 0 5 2 4 6 3 5 4 1 0 2 1 5 3 2 6 4 0 5 0 4 6 2 3 1 2 4 0 1 3 6 5 n=8, a(8)=112 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 Way of finding: brute force 0 1 2 3 4 5 6 7 4 2 1 7 0 6 5 3 5 7 3 2 6 0 4 1 7 5 6 4 3 1 2 0 6 3 7 1 5 4 0 2 1 0 4 6 2 7 3 5 3 6 5 0 7 2 1 4 2 4 0 5 1 3 7 6 n=9, a(9)=72 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 Way of finding: brute force using X-based fillings 0 1 2 3 4 5 6 7 8 6 8 3 4 7 2 0 5 1 5 7 6 1 8 0 2 4 3 7 3 8 2 5 4 1 0 6 2 4 0 8 1 3 5 6 7 4 5 1 6 0 7 3 8 2 8 6 7 5 3 1 4 2 0 1 0 5 7 2 6 8 3 4 3 2 4 0 6 8 7 1 5 n=10, a(10)>=109 Announcement: https://vk.com/wall162891802_2643, Eduard I. Vatutin, Jan 31 2024 Way of finding: neighborhoods of different special types of LS and DLS 0 1 2 3 4 5 6 7 8 9 1 2 3 0 5 4 8 9 6 7 4 6 5 7 0 2 1 3 9 8 3 7 1 6 8 9 5 4 2 0 7 3 6 1 9 8 2 0 5 4 5 8 4 9 1 3 0 2 7 6 8 5 9 4 3 1 7 6 0 2 6 4 7 5 2 0 9 8 1 3 9 0 8 2 7 6 3 1 4 5 2 9 0 8 6 7 4 5 3 1 n=11, a(11)>=172 Announcement: https://vk.com/wall162891802_2636, Eduard I. Vatutin, Jan 23 2024 Way of finding: diagonalizing of known LS from R. Bean 0 1 2 3 4 5 6 7 8 9 10 1 2 0 4 3 6 5 9 10 7 8 2 0 1 7 9 10 8 3 6 4 5 6 10 9 8 1 3 7 0 2 5 4 10 6 8 5 7 2 1 4 9 3 0 8 9 10 6 5 4 3 2 0 1 7 5 3 7 1 8 0 9 10 4 6 2 7 4 5 2 10 9 0 6 3 8 1 4 7 3 9 0 8 10 1 5 2 6 3 5 4 0 6 1 2 8 7 10 9 9 8 6 10 2 7 4 5 1 0 3 n=12, a(12)>=324 Announcement: https://vk.com/wall162891802_2669, Eduard I. Vatutin, Feb 23 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 1 2 0 4 9 7 8 10 11 3 5 6 2 0 1 9 3 10 11 5 6 4 7 8 8 6 11 10 7 9 1 4 0 5 3 2 11 8 6 7 5 4 2 3 1 10 9 0 4 3 9 1 0 11 10 8 7 2 6 5 10 7 5 8 6 2 4 1 3 11 0 9 9 4 3 2 1 8 7 6 5 0 11 10 5 10 7 6 11 0 3 2 9 8 1 4 6 11 8 5 10 3 0 9 2 7 4 1 3 9 4 0 2 6 5 11 10 1 8 7 7 5 10 11 8 1 9 0 4 6 2 3 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_2674, 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 3 11 0 5 4 7 13 10 12 8 2 9 6 3 0 4 1 2 11 13 6 9 8 12 5 10 7 12 8 6 9 7 13 11 4 1 0 3 10 5 2 9 10 8 12 13 7 2 5 3 4 1 6 0 11 8 12 13 10 6 2 4 11 0 3 9 7 1 5 10 9 7 8 11 6 5 2 12 1 0 13 3 4 4 11 3 5 9 0 8 12 2 13 6 1 7 10 5 2 1 4 0 12 10 9 6 7 11 3 13 8 11 4 5 2 1 3 12 8 7 10 13 0 6 9 2 5 0 11 3 1 9 10 13 6 7 4 8 12 7 6 10 13 12 9 1 0 11 5 2 8 4 3 13 7 9 6 8 10 3 1 4 2 5 12 11 0 6 13 12 7 10 8 0 3 5 11 4 9 2 1 n=15, a(15)>=630 Announcement: https://vk.com/wall162891802_2676, 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 4 6 9 8 0 12 1 11 3 2 14 13 5 7 10 12 8 14 6 5 4 3 13 1 10 9 7 0 11 2 2 3 0 7 9 10 11 1 13 4 5 6 14 8 12 6 4 11 12 1 8 0 9 5 14 13 2 3 10 7 10 7 5 1 14 2 13 3 11 12 0 8 9 6 4 3 5 7 0 8 1 12 10 4 13 2 14 6 9 11 14 13 12 11 10 9 7 8 6 5 4 3 2 1 0 11 9 6 14 12 13 2 4 10 1 8 0 7 5 3 13 14 8 9 7 11 10 12 2 3 6 5 4 0 1 8 12 13 4 3 6 5 14 0 7 11 10 1 2 9 1 0 10 5 6 3 4 2 12 11 7 9 8 14 13 5 2 1 10 11 7 9 0 14 6 3 4 13 12 8 7 10 3 2 13 0 14 5 9 8 1 12 11 4 6 9 11 4 13 2 14 8 6 7 0 12 1 10 3 5 n=16, a(16)>=960 Announcement: https://vk.com/wall162891802_2583, 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 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: Gergely method for random DLS of order 8, neighborhoods expanding using intercalate/loop rotation 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)>=431 Announcement: https://vk.com/wall162891802_2642, Eduard I. Vatutin, Jan 29 2024 Way of finding: neighborhoods of different special types of DLS 0 1 2 3 12 5 6 7 8 9 10 11 4 13 14 15 16 17 1 2 0 4 5 6 11 8 15 13 17 10 16 3 7 9 14 12 7 6 17 0 9 15 1 10 2 11 4 14 3 12 16 5 13 8 11 13 1 9 17 12 2 14 16 3 5 0 7 15 10 4 8 6 17 15 4 11 7 14 3 12 6 2 8 13 9 0 5 1 10 16 12 17 5 14 0 11 10 13 4 8 2 9 15 7 3 16 6 1 9 16 10 7 11 0 5 17 3 15 1 12 13 14 6 8 4 2 13 12 11 10 14 3 0 16 5 1 9 2 8 6 4 17 7 15 10 0 9 13 15 2 12 6 14 4 11 3 1 16 8 7 17 5 15 8 6 5 10 7 4 9 1 12 16 17 14 11 0 2 3 13 5 4 16 15 1 17 8 11 13 14 6 7 0 9 12 3 2 10 6 11 15 2 16 8 13 3 17 10 14 4 5 1 9 0 12 7 4 3 13 1 8 16 15 5 12 0 7 6 10 2 17 11 9 14 3 10 12 16 2 1 17 4 9 7 0 5 6 8 13 14 15 11 16 5 14 6 3 4 7 1 11 17 13 8 2 10 15 12 0 9 2 9 3 8 6 10 14 15 7 16 12 1 17 4 11 13 5 0 14 7 8 12 13 9 16 0 10 5 3 15 11 17 2 6 1 4 8 14 7 17 4 13 9 2 0 6 15 16 12 5 1 10 11 3 n=19, a(19)>=342 Announcement: https://vk.com/wall162891802_2603, Eduard I. Vatutin, Jan 09 2024 Way of finding: pandiagonal LS, different DLS with same number of intercalates was found in neighborhoods of different special types of DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 13 17 5 6 14 0 9 3 4 11 15 7 16 2 10 18 12 1 8 11 10 8 9 3 18 17 15 14 0 16 12 4 1 6 7 13 2 5 9 16 7 11 15 14 13 8 12 18 17 1 2 0 5 3 4 10 6 3 15 1 4 16 12 18 10 11 2 13 8 5 6 17 9 14 0 7 4 14 12 5 0 1 2 13 7 16 6 10 11 9 3 8 15 18 17 8 0 18 2 9 17 5 6 10 4 1 3 7 16 15 14 11 12 13 10 11 17 13 6 15 8 9 3 7 0 5 14 4 1 12 18 16 2 6 7 16 8 10 3 12 11 15 14 4 17 9 18 0 5 2 13 1 5 3 4 1 11 7 14 2 16 12 18 0 8 15 13 17 9 6 10 7 9 14 0 5 16 4 18 6 1 2 13 17 11 12 10 8 15 3 14 4 15 18 17 9 1 0 13 3 5 6 10 8 16 2 7 11 12 2 18 0 12 13 8 15 5 17 10 14 9 3 7 11 1 6 4 16 1 6 13 17 2 10 11 12 9 8 7 18 15 14 4 16 5 3 0 17 5 3 10 8 6 7 16 2 15 11 4 13 12 18 0 1 9 14 18 8 9 14 7 11 3 4 1 6 12 16 0 10 2 13 17 5 15 12 13 11 15 18 4 16 14 0 5 3 2 1 17 7 6 10 8 9 15 2 10 16 12 13 0 1 18 17 9 14 6 5 8 4 3 7 11 16 12 6 7 1 2 10 17 5 13 8 15 18 3 9 11 0 14 4 n=20, a(20)>=1100 Announcement: https://vk.com/wall162891802_2616, Eduard I. Vatutin, Jan 13 2024 Way of finding: neighborhoods expanding using intercalate/loop rotation, composite squares method with rotated subsquares 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 4 2 3 0 1 9 7 8 5 6 14 12 13 10 11 19 17 18 15 16 3 4 1 2 0 8 9 6 7 5 13 14 11 12 10 18 19 16 17 15 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 16 15 18 17 19 11 10 13 12 14 6 5 8 7 9 1 0 3 2 4 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 17 19 15 18 16 12 14 10 13 11 7 9 5 8 6 2 4 0 3 1 15 17 16 19 18 10 12 11 14 13 5 7 6 9 8 0 2 1 4 3 18 16 19 15 17 13 11 14 10 12 8 6 9 5 7 3 1 4 0 2 5 6 7 8 9 0 1 2 3 4 15 16 17 18 19 10 11 12 13 14 9 7 8 5 6 4 2 3 0 1 19 17 18 15 16 14 12 13 10 11 8 9 6 7 5 3 4 1 2 0 18 19 16 17 15 13 14 11 12 10 6 8 5 9 7 1 3 0 4 2 16 18 15 19 17 11 13 10 14 12 7 5 9 6 8 2 0 4 1 3 17 15 19 16 18 12 10 14 11 13 11 10 13 12 14 16 15 18 17 19 1 0 3 2 4 6 5 8 7 9 14 13 12 11 10 19 18 17 16 15 4 3 2 1 0 9 8 7 6 5 12 14 10 13 11 17 19 15 18 16 2 4 0 3 1 7 9 5 8 6 10 12 11 14 13 15 17 16 19 18 0 2 1 4 3 5 7 6 9 8 13 11 14 10 12 18 16 19 15 17 3 1 4 0 2 8 6 9 5 7 n=21, a(21)>=418 Announcement: -, Eduard I. Vatutin, Jan 30 2024 Way of finding: neighborhoods expanding using intercalate/loop rotation 0 1 2 3 4 5 14 7 8 9 10 11 12 13 6 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 18 9 0 3 14 17 20 11 2 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 20 2 1 7 11 13 9 18 0 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 16 17 12 15 10 9 14 19 6 11 1 5 8 3 4 7 0 2 16 11 17 13 10 14 0 8 18 15 5 1 2 12 20 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 6 11 12 13 2 7 8 9 14 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 12 20 16 2 14 17 11 7 9 3 6 18 4 0 8 19 1 15 n=22, a(22)>=747 Announcement: -, Eduard I. Vatutin, Feb 01 2024 Way of finding: neighborhoods of special types of DLS 0 1 2 18 4 5 6 8 7 9 10 11 12 14 13 15 16 17 3 19 20 21 17 5 1 9 10 21 19 6 13 18 7 14 3 8 15 2 0 11 12 20 16 4 7 15 9 1 13 10 17 18 0 2 5 16 19 21 3 4 11 8 20 12 6 14 10 12 6 13 14 2 0 5 17 20 18 3 1 4 16 21 19 7 8 15 9 11 4 16 20 12 15 0 14 11 2 3 13 8 18 19 10 7 21 6 9 1 5 17 11 9 15 4 21 14 2 16 8 1 3 18 20 13 5 19 7 0 17 6 12 10 2 13 5 17 0 18 7 20 6 10 9 12 11 15 1 14 3 21 4 16 8 19 18 14 8 10 12 15 16 2 20 17 21 0 4 1 19 5 6 9 11 13 7 3 13 2 3 7 16 17 12 21 11 15 20 1 6 10 0 9 4 5 14 18 19 8 15 3 11 0 20 12 13 14 19 16 4 17 5 2 7 8 9 1 21 10 18 6 19 4 16 21 1 3 8 7 15 11 12 9 10 6 14 13 18 20 0 5 17 2 9 11 7 6 3 8 20 4 16 0 2 19 21 5 17 1 13 18 15 14 10 12 20 21 4 16 7 19 10 12 18 13 6 15 8 3 9 11 2 14 5 17 0 1 6 18 10 8 2 9 21 1 4 5 14 7 16 17 20 0 12 19 13 11 3 15 12 10 14 15 18 13 1 17 5 21 19 2 0 16 4 20 8 3 6 7 11 9 21 20 19 3 17 16 15 13 14 12 11 10 9 7 8 6 5 4 18 2 1 0 5 17 21 2 6 1 3 10 12 14 8 13 7 9 11 18 20 15 19 0 4 16 16 8 0 19 11 20 18 15 9 7 17 4 14 12 6 3 1 10 2 21 13 5 14 6 12 20 8 11 4 3 21 19 16 5 2 0 18 17 10 13 1 9 15 7 8 19 18 14 5 4 9 0 10 6 1 20 15 11 21 12 17 16 7 3 2 13 1 0 17 5 19 7 11 9 3 8 15 6 13 18 12 10 14 2 16 4 21 20 3 7 13 11 9 6 5 19 1 4 0 21 17 20 2 16 15 12 10 8 14 18 n=23, a(23)>=899 Announcement: https://vk.com/wall162891802_2645, Eduard I. Vatutin, Feb 04 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 5 16 1 8 9 10 0 21 2 3 4 15 18 19 20 11 22 12 13 14 7 6 17 12 22 7 2 1 4 5 16 21 8 9 3 13 14 15 6 17 18 19 20 11 0 10 18 17 16 21 8 9 1 22 7 2 3 12 19 20 11 0 10 13 14 15 6 5 4 13 10 22 7 2 3 18 17 16 21 1 8 14 15 6 5 4 19 20 11 0 12 9 19 4 17 1 21 14 13 10 22 7 2 6 20 11 0 12 9 8 15 16 5 18 3 14 9 10 22 7 2 19 1 17 16 21 18 15 6 5 4 3 20 11 0 12 13 8 1 3 4 17 16 21 14 9 10 22 7 20 11 0 12 13 8 15 6 5 18 19 2 15 8 9 10 22 7 20 19 4 1 16 17 6 5 18 3 2 11 0 12 13 14 21 11 2 3 4 17 16 15 8 1 10 22 13 0 12 9 14 21 6 5 18 19 20 7 6 21 8 9 10 1 11 2 3 4 17 22 5 18 19 20 7 0 12 13 14 15 16 20 15 11 6 3 22 12 18 13 17 8 1 10 9 4 19 0 14 21 7 16 2 5 21 6 5 18 19 20 7 0 12 13 14 9 8 1 10 22 11 2 3 4 17 16 15 7 0 12 13 14 15 16 5 18 19 20 4 2 3 1 17 6 21 8 9 10 22 11 16 5 18 19 20 11 22 12 9 14 15 0 21 8 13 10 1 7 2 3 4 17 6 22 12 13 14 15 6 17 4 19 20 11 21 7 2 3 18 5 16 1 8 9 10 0 17 18 19 20 11 0 10 13 14 15 6 5 16 21 8 9 12 22 7 2 3 4 1 10 13 14 15 6 17 4 3 20 11 0 19 22 7 2 1 18 5 16 21 8 9 12 4 19 20 11 0 12 9 14 15 6 5 7 17 16 21 8 13 10 22 1 2 3 18 9 14 15 16 5 18 3 20 11 0 12 10 1 22 7 2 19 4 17 6 21 8 13 3 20 21 0 12 13 8 11 6 5 18 2 4 17 16 7 14 9 10 22 15 1 19 8 7 6 5 18 19 2 15 0 12 13 16 9 10 22 21 20 3 4 17 1 11 14 2 11 0 12 13 8 21 6 5 18 19 14 3 4 17 16 15 1 9 10 22 7 20 n=24, a(24)>=1680 Announcement: 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 4 2 5 0 3 1 10 8 11 6 9 7 16 14 17 12 15 13 22 20 23 18 21 19 3 5 1 2 0 4 9 11 7 8 6 10 15 17 13 14 12 16 21 23 19 20 18 22 5 3 0 4 1 2 11 9 6 10 7 8 17 15 12 16 13 14 23 21 18 22 19 20 2 4 3 1 5 0 8 10 9 7 11 6 14 16 15 13 17 12 20 22 21 19 23 18 1 0 4 5 2 3 7 6 10 11 8 9 13 12 16 17 14 15 19 18 22 23 20 21 22 20 19 21 18 23 16 14 13 15 12 17 10 8 7 9 6 11 4 2 1 3 0 5 18 19 23 22 21 20 12 13 17 16 15 14 6 7 11 10 9 8 0 1 5 4 3 2 21 23 20 19 22 18 15 17 14 13 16 12 9 11 8 7 10 6 3 5 2 1 4 0 23 21 22 18 20 19 17 15 16 12 14 13 11 9 10 6 8 7 5 3 4 0 2 1 19 18 21 20 23 22 13 12 15 14 17 16 7 6 9 8 11 10 1 0 3 2 5 4 20 22 18 23 19 21 14 16 12 17 13 15 8 10 6 11 7 9 2 4 0 5 1 3 6 7 8 9 10 11 0 1 2 3 4 5 18 19 20 21 22 23 12 13 14 15 16 17 10 8 11 6 9 7 4 2 5 0 3 1 22 20 23 18 21 19 16 14 17 12 15 13 9 11 7 8 6 10 3 5 1 2 0 4 21 23 19 20 18 22 15 17 13 14 12 16 11 9 6 10 7 8 5 3 0 4 1 2 23 21 18 22 19 20 17 15 12 16 13 14 8 10 9 7 11 6 2 4 3 1 5 0 20 22 21 19 23 18 14 16 15 13 17 12 7 6 10 11 8 9 1 0 4 5 2 3 19 18 22 23 20 21 13 12 16 17 14 15 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 16 14 17 12 15 13 22 20 23 18 21 19 4 2 5 0 3 1 10 8 11 6 9 7 15 17 13 14 12 16 21 23 19 20 18 22 3 5 1 2 0 4 9 11 7 8 6 10 17 15 12 16 13 14 23 21 18 22 19 20 5 3 0 4 1 2 11 9 6 10 7 8 14 16 15 13 17 12 20 22 21 19 23 18 2 4 3 1 5 0 8 10 9 7 11 6 13 12 16 17 14 15 19 18 22 23 20 21 1 0 4 5 2 3 7 6 10 11 8 9 n=25, a(25)>=264 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 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 Mar 11 2024