A033047 Sums of distinct powers of 11.

0, 1, 11, 12, 121, 122, 132, 133, 1331, 1332, 1342, 1343, 1452, 1453, 1463, 1464, 14641, 14642, 14652, 14653, 14762, 14763, 14773, 14774, 15972, 15973, 15983, 15984, 16093, 16094, 16104, 16105, 161051, 161052, 161062, 161063, 161172

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

Numbers without any base-11 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.

Crossrefs

Cf. A000695, A005836, A033042-A033052.

Row 10 of array A104257.

Programs

Mathematica

With[{k = 11}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* Michael De Vlieger, Oct 28 2022 *)

PARI

{for(vv=0,35,
bvv=binary(vv);
texp=0;btb=0;
forstep(i=length(bvv),1,-1,btb=btb+bvv[i]*11^texp;texp++);
print1(btb,", "))} \\ Douglas Latimer, May 12 2012

PARI

a(n)=fromdigits(binary(n),11) \\ Charles R Greathouse IV, Jan 11 2017

Formula

a(n) = Sum_{i=0..m} d(i)*11^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.

a(n) = A097257(n)/10.

a(2n) = 11*a(n), a(2n+1) = a(2n)+1.

a(n) = Sum_{k>=0} A030308(n,k)*11^k. - Philippe Deléham, Oct 17 2011

G.f.: (1/(1 - x))*Sum_{k>=0} 11^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

Extensions

Extended by Ray Chandler, Aug 03 2004