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A033049 Sums of distinct powers of 13. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Numbers without any base-13 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)*13^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., m} 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

PROG

(PARI) A033049(n, b=13)=subst(Pol(binary(n)), 'x, b) \\ M. F. Hasler, Feb 01 2016

CROSSREFS

Cf. A000695, A005836, A033042-A033052.

Row 12 of array A104257.

Sequence in context: A041356 A103868 A041358 * A249313 A041083 A041360

Adjacent sequences:  A033046 A033047 A033048 * A033050 A033051 A033052

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Extended by Ray Chandler, Aug 03 2004

STATUS

approved

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Last modified February 23 15:43 EST 2018. Contains 299581 sequences. (Running on oeis4.)