A033051 Numbers whose set of base 15 digits is {0,1}.

0, 1, 15, 16, 225, 226, 240, 241, 3375, 3376, 3390, 3391, 3600, 3601, 3615, 3616, 50625, 50626, 50640, 50641, 50850, 50851, 50865, 50866, 54000, 54001, 54015, 54016, 54225, 54226, 54240, 54241, 759375, 759376, 759390, 759391, 759600

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

Sums of distinct powers of 15.

a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - Philippe Deléham, Oct 17 2011.

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 14 of array A104257.

Programs

Mathematica

With[{k = 15}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* Michael De Vlieger, Oct 28 2022 *)
FromDigits[#,15]&/@Tuples[{0,1},6] (* Harvey P. Dale, Sep 15 2024 *)

PARI

A033051(n, b=15)=subst(Pol(binary(n)),'x,b) \\ M. F. Hasler, Feb 01 2016

Formula

a(n) = Sum_{i=0..m} d(i)*15^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.

a(n) = A097261(n)/14.

a(2n) = 15*a(n), a(2n+1) = a(2n)+1.

a(n) = Sum_{k>=0} A030308(n,k)*15^k. - Philippe Deléham, Oct 17 2011.

G.f.: (1/(1 - x))*Sum_{k>=0} 15^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

Extensions

Extended by Ray Chandler, Aug 03 2004