A097253 Numbers whose set of base 7 digits is {0,6}.

0, 6, 42, 48, 294, 300, 336, 342, 2058, 2064, 2100, 2106, 2352, 2358, 2394, 2400, 14406, 14412, 14448, 14454, 14700, 14706, 14742, 14748, 16464, 16470, 16506, 16512, 16758, 16764, 16800, 16806, 100842, 100848, 100884, 100890, 101136

Offset: 1

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 7 for every i.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A001196, A005823, A097251-A097262.

Programs

Magma

[n: n in [0..200000] | Set(IntegerToSequence(n, 7)) subset {0, 6}]; // Vincenzo Librandi, May 25 2012

Mathematica

fQ[n_]:=Union@Join[{0,6},IntegerDigits[n,7]]=={0,6};Select[Range[0,140000],fQ] (* Vincenzo Librandi, May 25 2012 *)
FromDigits[#,7]&/@Tuples[{0,6},6] (* This program is several thousand times faster than the first program, above. *) (* Harvey P. Dale, Aug 12 2023 *)

Maxima

a[0]:0$ a[n]:=7*a[floor(n/2)]+3*(1-(-1)^n)$ makelist(a[n], n, 0, 36); /* Bruno Berselli, May 25 2012 */

Formula

a(n) = 6*A033044(n).

a(2n) = 7*a(n), a(2n+1) = a(2n)+6.

Extensions

Offset corrected by Arkadiusz Wesolowski, Nov 09 2013