A097259 Numbers whose set of base 13 digits is {0,C}, where C base 13 = 12 base 10.

0, 12, 156, 168, 2028, 2040, 2184, 2196, 26364, 26376, 26520, 26532, 28392, 28404, 28548, 28560, 342732, 342744, 342888, 342900, 344760, 344772, 344916, 344928, 369096, 369108, 369252, 369264, 371124, 371136, 371280, 371292, 4455516

Offset: 0

Author

Ray Chandler, Aug 03 2004

Keywords

• nonn
• base

Comments

n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a power of 13 for every i.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001196, A005823, A097251-A097262.

Programs

Magma

[n: n in [0..4500000] | Set(IntegerToSequence(n, 13)) subset {0, 12}]; // Vincenzo Librandi, Jun 04 2012

Mathematica

f[n_] := FromDigits[ IntegerDigits[n, 2] /. {1 -> 12}, 13]; Array[f, 33, 0] (* or much slower *)
fQ[n_] := Union@ Join[{0, 12}, IntegerDigits[n, 13]] == {0, 12}; Select[ Range[0, 4455516 ], fQ] (* Robert G. Wilson v, May 12 2012 *)
FromDigits[#,13]&/@Tuples[{0,12},5] (* Vincenzo Librandi, Jun 04 2012 *)

Formula

a(n) = 12*A033049(n).

a(2n) = 13*a(n), a(2n+1) = a(2n)+12.