Minimum number of intercalates in a diagonal Latin square of order n, https://oeis.org/A307163

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: brute force
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)=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: brute force
0 1 2 3 4
4 2 3 0 1
3 4 1 2 0
1 3 0 4 2
2 0 4 1 3

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)=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: brute force
0 1 2 3 4 5 6
4 2 6 0 5 1 3
3 5 1 6 0 4 2
5 6 3 4 1 2 0
6 4 5 2 3 0 1
1 3 0 5 2 6 4
2 0 4 1 6 3 5

n=8, a(8)=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: brute force
0 1 2 3 4 5 6 7
3 2 5 1 6 7 0 4
6 4 1 0 7 2 5 3
2 7 3 4 5 0 1 6
7 5 0 6 3 4 2 1
5 0 4 7 1 6 3 2
4 3 6 5 2 1 7 0
1 6 7 2 0 3 4 5

n=9, a(9)=0
Announcement: 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: 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
Way of finding: cyclic diagonal 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 squares
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
Way of finding: cyclic diagonal 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_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 13 7 8 10 2 9 12 4 5 11 0 6 3
13 2 4 6 9 12 0 8 11 3 1 5 10 7
5 7 8 10 11 3 13 6 0 2 9 1 4 12
12 8 11 0 5 10 3 9 13 4 2 7 1 6
9 5 12 4 6 7 11 3 10 1 0 13 8 2
3 6 0 13 1 4 2 11 5 8 7 12 9 10
4 11 5 2 12 13 8 1 7 0 6 10 3 9
10 9 13 7 3 0 4 5 12 11 8 6 2 1
8 10 1 5 2 9 7 0 3 6 12 4 13 11
6 4 9 1 7 11 12 13 2 10 3 8 5 0
11 0 3 12 8 1 10 2 6 13 4 9 7 5
2 12 6 9 0 8 5 10 1 7 13 3 11 4
7 3 10 11 13 6 1 4 9 12 5 2 0 8

n=15, a(15)=0
Announcement: https://vk.com/wall162891802_2476, Eduard I. Vatutin, Aug 06 2023
Way of finding: diagonalized cyclic DLS
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 2 0 4 5 3 7 13 9 14 11 12 10 6 8
10 11 12 13 6 7 1 2 4 5 9 14 8 0 3
13 6 7 14 8 9 4 5 12 10 0 1 2 3 11
5 3 4 10 11 12 14 8 1 2 7 13 6 9 0
12 10 11 7 13 6 0 1 3 4 8 9 14 2 5
3 4 5 11 12 10 8 9 2 0 13 6 7 14 1
6 7 13 8 9 14 5 3 10 11 1 2 0 4 12
14 8 9 1 2 0 12 10 7 13 3 4 5 11 6
4 5 3 12 10 11 9 14 0 1 6 7 13 8 2
8 9 14 2 0 1 10 11 13 6 4 5 3 12 7
2 0 1 5 3 4 13 6 14 8 12 10 11 7 9
11 12 10 6 7 13 2 0 5 3 14 8 9 1 4
7 13 6 9 14 8 3 4 11 12 2 0 1 5 10
9 14 8 0 1 2 11 12 6 7 5 3 4 10 13

n=16, a(16)<=5
Announcement: https://vk.com/wall162891802_2586, Eduard I. Vatutin, Dec 29 2023
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
3 13 1 6 0 14 15 11 12 8 7 10 4 5 9 2
8 4 10 11 3 0 9 1 2 15 14 13 7 12 5 6
15 0 14 2 10 7 11 8 5 4 12 9 13 6 1 3
6 2 15 14 1 11 4 5 7 3 13 8 10 9 12 0
9 3 8 5 11 6 7 2 13 14 0 12 1 10 15 4
7 15 6 10 8 12 5 9 0 1 2 14 3 4 13 11
5 6 7 15 2 9 13 14 10 12 11 3 0 1 4 8
13 5 12 0 15 8 1 4 9 10 3 2 14 11 6 7
4 12 3 1 7 13 2 0 15 11 6 5 9 14 8 10
2 8 9 4 13 3 10 12 14 7 15 6 5 0 11 1
10 9 13 12 6 2 14 3 11 0 1 4 15 8 7 5
11 14 4 7 5 10 12 15 3 6 9 1 8 2 0 13
1 10 5 9 12 15 3 6 4 13 8 0 11 7 2 14
12 11 0 13 14 4 8 10 1 2 5 7 6 15 3 9
14 7 11 8 9 1 0 13 6 5 4 15 2 3 10 12

n=17, a(17)=0
Announcement: -, Eduard I. Vatutin, before Aug 06 2023
Way of finding: cyclic DLS
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)<=10
Announcement: https://vk.com/wall162891802_2602, Eduard I. Vatutin, Jan 05 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
5 16 9 14 11 12 13 10 15 8 1 6 17 4 3 2 7 0
2 3 7 6 1 0 4 15 12 17 9 13 5 10 11 16 8 14
14 4 15 12 6 1 16 0 3 2 17 7 10 11 5 9 13 8
7 9 6 4 5 10 15 1 17 0 16 8 14 12 13 11 3 2
1 12 4 7 17 11 9 2 14 3 8 15 6 0 10 13 5 16
16 17 11 10 0 2 3 8 5 14 15 9 13 6 1 4 12 7
8 10 0 2 7 17 14 13 6 11 4 3 9 16 15 5 1 12
17 11 3 8 13 6 1 5 9 15 0 16 7 2 12 14 4 10
12 7 17 15 16 9 5 4 13 6 11 14 2 1 8 0 10 3
6 0 5 17 3 13 7 14 1 16 2 10 4 8 9 12 15 11
15 8 16 13 10 14 11 9 2 12 3 4 0 7 6 1 17 5
9 13 10 1 2 3 0 12 11 4 5 17 8 14 16 7 6 15
13 5 12 9 8 4 10 3 16 7 14 1 11 15 2 17 0 6
4 15 14 0 9 7 12 11 10 1 6 5 16 3 17 8 2 13
3 6 1 16 14 8 2 17 4 13 12 0 15 5 7 10 11 9
11 2 8 5 15 16 17 6 7 10 13 12 1 9 0 3 14 4
10 14 13 11 12 15 8 16 0 5 7 2 3 17 4 6 9 1

n=19, a(19)=0
Announcement: -, Eduard I. Vatutin, before Aug 06 2023
Way of finding: cyclic DLS
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)<=3
Announcement: -, Eduard I. Vatutin, Feb 02 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 
4 15 11 0 1 9 17 8 5 6 14 12 13 10 3 19 2 18 7 16 
7 4 1 15 0 8 9 6 2 5 13 14 11 12 10 18 19 16 17 3 
1 3 0 4 15 6 8 5 9 2 11 13 10 14 7 16 18 12 19 17 
15 0 4 1 17 2 5 9 6 8 7 10 14 3 13 11 12 19 16 18 
19 2 7 18 16 10 15 14 3 13 9 5 8 17 6 0 1 11 4 12 
16 17 18 11 2 13 14 19 10 12 6 8 15 9 5 7 3 4 0 1 
18 16 15 17 19 11 13 12 14 10 2 6 5 8 9 4 7 1 3 0 
17 18 19 16 11 0 3 10 13 14 5 2 9 6 8 1 4 7 12 15 
11 19 16 7 18 14 10 13 12 3 8 9 6 5 17 2 0 15 1 4 
9 8 6 2 5 7 4 17 0 1 16 19 18 11 12 10 15 3 14 13 
5 6 17 9 8 1 7 0 15 4 12 18 3 16 19 13 11 14 10 2 
2 5 8 6 9 12 1 4 17 15 3 7 19 18 16 14 13 0 11 10 
8 7 9 5 6 4 0 15 1 17 19 3 16 2 18 12 14 10 13 11 
6 9 5 8 7 17 12 1 4 0 18 16 2 19 11 3 10 13 15 14 
12 11 14 10 13 19 16 3 18 7 1 0 17 15 4 6 5 8 2 9 
13 14 10 12 3 15 19 18 11 16 4 17 7 1 0 9 8 2 6 5 
10 13 3 14 12 18 2 16 19 11 15 4 0 7 1 17 9 5 8 6 
3 10 12 13 14 16 18 11 7 19 0 15 1 4 2 5 17 6 9 8 
14 12 13 19 10 3 11 2 16 18 17 1 4 0 15 8 6 9 5 7 

n=21, a(21)<=11
Announcement: https://vk.com/wall162891802_2745, Eduard I. Vatutin, Apr 13 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
13 2 20 4 11 6 9 18 15 5 3 7 17 10 8 0 1 16 19 12 14
9 7 8 6 19 10 14 5 11 4 0 16 18 1 3 17 20 2 15 13 12
4 8 19 5 10 1 2 6 16 18 13 15 0 9 20 12 17 7 11 14 3
2 10 15 14 9 19 20 13 18 6 16 3 5 4 12 1 11 8 7 17 0
15 14 4 0 8 3 1 9 5 2 17 20 7 19 13 18 10 12 6 11 16
18 6 0 1 2 14 4 20 9 3 15 17 11 7 16 8 19 13 12 5 10
14 16 9 7 1 4 5 10 2 11 20 13 19 17 15 6 12 0 8 3 18
5 4 10 8 16 2 3 19 20 0 12 1 13 11 18 14 9 15 17 6 7
20 0 16 9 5 18 10 2 4 19 8 14 6 12 17 7 15 11 3 1 13
19 12 7 17 18 11 15 16 1 13 6 8 9 3 0 10 14 4 2 20 5
3 19 13 18 15 17 16 0 7 1 4 12 14 20 11 2 8 6 5 10 9
8 3 17 13 12 20 18 11 19 16 14 5 1 0 2 9 6 10 4 7 15
17 9 5 11 3 12 0 4 13 14 18 10 15 16 6 19 7 1 20 8 2
6 11 18 20 13 15 8 12 0 17 1 2 10 14 7 3 5 19 9 16 4
12 17 6 15 7 9 19 1 14 20 2 0 3 18 10 11 13 5 16 4 8
1 15 14 12 0 8 13 17 3 7 11 6 16 2 5 4 18 20 10 9 19
16 13 11 2 17 0 7 15 10 12 19 4 8 5 9 20 3 14 1 18 6
7 20 3 10 6 16 12 14 17 8 9 19 4 15 1 5 2 18 13 0 11
11 5 12 19 20 13 17 3 6 10 7 18 2 8 4 16 0 9 14 15 1
10 18 1 16 14 7 11 8 12 15 5 9 20 6 19 13 4 3 0 2 17

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 DLS
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: 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 13 2024