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

0,3

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.

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000695, A005836, A033042-A033052.

Row 10 of array A104257.

Sequence in context: A296447 A110380 A164854 * A094624 A108218 A038326

Adjacent sequences: A033044 A033045 A033046 * A033048 A033049 A033050

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

Extended by Ray Chandler, Aug 03 2004

Status

approved