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

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

1,2

Comments

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.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Circulant Matrix

Wikipedia, Circulant matrix

Example

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 |

Mathematica

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

Prog

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

Crossrefs

Cf. A177894, A239019, A317291.

Sequence in context: A377948 A226467 A244394 * A115853 A050785 A369347

Adjacent sequences: A299789 A299790 A299791 * A299793 A299794 A299795

Keyword

nonn,base

Author

Jianing Song, Jan 21 2019

Status

approved