A033046 Sums of distinct powers of 9.
0, 1, 9, 10, 81, 82, 90, 91, 729, 730, 738, 739, 810, 811, 819, 820, 6561, 6562, 6570, 6571, 6642, 6643, 6651, 6652, 7290, 7291, 7299, 7300, 7371, 7372, 7380, 7381, 59049, 59050, 59058, 59059, 59130, 59131, 59139, 59140, 59778, 59779, 59787
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
FromDigits[#,9]&/@Tuples[{1,0},6]//Sort (* Harvey P. Dale, Sep 05 2017 *) -
PARI
A033046(n,b=9)=subst(Pol(binary(n)),'x,b) \\ M. F. Hasler, Feb 01 2016
Formula
a(n) = Sum_{i=0..m} d(i)*9^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
a(n) = A097255(n)/8.
a(2n) = 9*a(n), a(2n+1) = a(2n)+1.
a(n) = Sum_{k>=0} A030308(n,k)*9^k. - Philippe Deléham, Oct 17 2011
G.f.: (1/(1 - x))*Sum_{k>=0} 9^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017
Extensions
Extended by Ray Chandler, Aug 03 2004
Comments