A033049 Sums of distinct powers of 13.

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

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

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)*13^i, where Sum_{i=0..m} d(i)*2^i 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

Mathematica

With[{k = 13}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* Michael De Vlieger, Oct 28 2022 *)

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