A317291 Numbers k not in A239019 such that A177894(k) = 0.

0, 1001, 1012, 1023, 1034, 1045, 1056, 1067, 1078, 1089, 1100, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 1210, 1221, 1232, 1243, 1254, 1265, 1276, 1287, 1298, 1320, 1331, 1342, 1353, 1364, 1375, 1386, 1397, 1430, 1441, 1452, 1463, 1474, 1485, 1496

Offset

1,2

Comments

Of course A177894(A239019(n)) = 0 because the corresponding circular matrices each contains at least two identical rows or columns. This sequence gives the other numbers.

A four-digit number abcd is in this sequence if and only if a + c = b + d and (a != c or b != d).

Links

Table of n, a(n) for n=1..43.

Eric Weisstein's World of Mathematics, Circulant Matrix.

Wikipedia, Circulant matrix.

Example

2178 is a term because the value of the following determinant is 0, although the determinant itself contains no identical rows or columns:
| 2 1 7 8 |
| 1 7 8 2 |
| 7 8 2 1 |
| 8 2 1 7 |

Prog

(PARI) for(n=0, 1500, if(!n ||(n&!A177894(n)&&!A239019(n)), print1(n, ", "))) \\ See A177894 and A239019 for their programs

Crossrefs

Cf. A177894, A239019, A299792.

Sequence in context: A262859 A044881 A291269 * A362921 A241946 A100846

Adjacent sequences: A317288 A317289 A317290 * A317292 A317293 A317294

Keyword

nonn,base

Author

Jianing Song, Jan 21 2019

Status

approved