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A033046
Sums of distinct powers of 9.
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
0,3
COMMENTS
Numbers without any base-9 digits greater than 1.
a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - Philippe Deléham, Oct 17 2011
LINKS
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.
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
MATHEMATICA
FromDigits[#, 9]&/@Tuples[{1, 0}, 6]//Sort (* Harvey P. Dale, Sep 05 2017 *)
PROG
(PARI) A033046(n, b=9)=subst(Pol(binary(n)), 'x, b) \\ M. F. Hasler, Feb 01 2016
CROSSREFS
Row 9 of array A104257.
Sequence in context: A098325 A101242 A342615 * A025635 A116555 A038300
KEYWORD
nonn,base,easy
EXTENSIONS
Extended by Ray Chandler, Aug 03 2004
STATUS
approved