A033049 Sums of distinct powers of 13.
0, 1, 13, 14, 169, 170, 182, 183, 2197, 2198, 2210, 2211, 2366, 2367, 2379, 2380, 28561, 28562, 28574, 28575, 28730, 28731, 28743, 28744, 30758, 30759, 30771, 30772, 30927, 30928, 30940, 30941, 371293, 371294, 371306, 371307, 371462
Offset: 0
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.
Programs
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Mathematica
With[{k = 13}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* Michael De Vlieger, Oct 28 2022 *) -
PARI
A033049(n,b=13)=subst(Pol(binary(n)),'x,b) \\ M. F. Hasler, Feb 01 2016
Formula
a(n) = Sum_{i=0..m} d(i)*13^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
a(n) = A097259(n)/12.
a(2n) = 13*a(n), a(2n+1) = a(2n)+1.
a(n) = Sum_{k>=0} A030308(n,k)*13^k. - Philippe Deléham, Oct 17 2011
G.f.: (1/(1 - x))*Sum_{k>=0} 13^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017
Extensions
Extended by Ray Chandler, Aug 03 2004
Comments