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A033046 Sums of distinct powers of 9. 7
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 (list; graph; refs; listen; history; text; internal format)
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

FORMULA

a(n) = Sum{d(i)*9^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., m} 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: A135332 A098325 A101242 * 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

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Last modified October 21 09:27 EDT 2018. Contains 316408 sequences. (Running on oeis4.)