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

0,3

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

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.

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

Cf. A000695, A005836, A033043-A033052.

Row 9 of array A104257.

Sequence in context: A098325 A101242 A342615 * A025635 A116555 A038300

Adjacent sequences: A033043 A033044 A033045 * A033047 A033048 A033049

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

Extended by Ray Chandler, Aug 03 2004

Status

approved