A033050 Numbers whose set of base 14 digits is {0,1}.

0, 1, 14, 15, 196, 197, 210, 211, 2744, 2745, 2758, 2759, 2940, 2941, 2954, 2955, 38416, 38417, 38430, 38431, 38612, 38613, 38626, 38627, 41160, 41161, 41174, 41175, 41356, 41357, 41370, 41371, 537824, 537825, 537838, 537839, 538020

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Sums of distinct powers of 14.

The base-14 digits may comprise zero, one, or both. - Harvey P. Dale, May 12 2014

Links

• T. D. Noe, Table of n, a(n) for n = 0..1023
• Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 45.

Crossrefs

Cf. A000695, A005836, A033042-A033052.

Row 13 of array A104257.

Programs

Mathematica

Select[Range[0,540000],Max[IntegerDigits[#,14]]<2&] (* Harvey P. Dale, May 12 2014 *)
FromDigits[#,14]&/@Tuples[{0,1},6] (* Harvey P. Dale, Jun 18 2021 *)

PARI

A033050(n,b=14)=subst(Pol(binary(n)),'x,b) \\ M. F. Hasler, Feb 01 2016

Formula

a(n) = Sum_{i=0..m} d(i)*14^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.

a(n) = A097260(n)/13.

a(2n) = 14*a(n), a(2n+1) = a(2n)+1.

a(n) = Sum_{k>=0} A030308(n,k)*14^k. - Philippe Deléham, Oct 20 2011

G.f.: (1/(1 - x))*Sum_{k>=0} 14^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

Extensions

Extended by Ray Chandler, Aug 03 2004