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

%I A299792 #92 Feb 16 2025 08:33:53
%S A299792 0,11,22,33,44,55,66,77,88,99,111,222,333,444,555,666,777,888,999,
%T A299792 1001,1010,1012,1023,1034,1045,1056,1067,1078,1089,1100,1111,1122,
%U A299792 1133,1144,1155,1166,1177,1188,1199,1210,1212,1221,1232,1243,1254,1265,1276,1287,1298,1313
%N A299792 Numbers k such that A177894(k) = 0.
%C A299792 A one-digit number a is in this sequence if and only if a = 0.
%C A299792 A two-digit number ab is in this sequence if and only if a = b.
%C A299792 A three-digit number abc is in this sequence if and only if a = b = c.
%C A299792 A four-digit number abcd is in this sequence if and only if a + c = b + d or (a = c and b = d)
%C A299792 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.
%H A299792 Paolo Xausa, <a href="/A299792/b299792.txt">Table of n, a(n) for n = 1..10000</a>
%H A299792 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CirculantMatrix.html">Circulant Matrix</a>
%H A299792 Wikipedia, <a href="http://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>
%e A299792 1452 is a term because the value of the following determinant is 0:
%e A299792   | 1 4 5 2 |
%e A299792   | 4 5 2 1 |
%e A299792   | 5 2 1 4 |
%e A299792   | 2 1 4 5 |
%t A299792 A299792Q[k_] := k == 0 || Det[NestList[RotateLeft, IntegerDigits[k], IntegerLength[k]-1]] == 0; Select[Range[0, 2000], A299792Q] (* _Paolo Xausa_, Mar 11 2024 *)
%o A299792 (PARI) for(n=0, 1500, if(!A177894(n), print1(n, ", "))) \\ See A177894 for its program
%Y A299792 Cf. A177894, A239019, A317291.
%K A299792 nonn,base
%O A299792 1,2
%A A299792 _Jianing Song_, Jan 21 2019