A317291 -id:A317291 - cp's OEIS frontend

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1001, 1010, 1012, 1023, 1034, 1045, 1056, 1067, 1078, 1089, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 1210, 1212, 1221, 1232, 1243, 1254, 1265, 1276, 1287, 1298, 1313

Offset: 1

Jianing Song, Jan 21 2019

A one-digit number a is in this sequence if and only if a = 0.
A two-digit number ab is in this sequence if and only if a = b.
A three-digit number abc is in this sequence if and only if a = b = c.
A four-digit number abcd is in this sequence if and only if a + c = b + d or (a = c and b = d)
A239019 is trivially a subsequence (because the corresponding circular matrices each contains at least two identical rows or columns). {a(n)} \ A239019 is given as A317291.

			1452 is a term because the value of the following determinant is 0:
  | 1 4 5 2 |
  | 4 5 2 1 |
  | 5 2 1 4 |
  | 2 1 4 5 |

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Circulant Matrix
Wikipedia, Circulant matrix

Cf. A177894, A239019, A317291.

A299792Q[k_] := k == 0 || Det[NestList[RotateLeft, IntegerDigits[k], IntegerLength[k]-1]] == 0; Select[Range[0, 2000], A299792Q] (* Paolo Xausa, Mar 11 2024 *)

for(n=0, 1500, if(!A177894(n), print1(n, ", "))) \\ See A177894 for its program

cp's OEIS Frontend

A299792 Numbers k such that A177894(k) = 0.

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