A197351 a(0)=0, a(1)=1, a(2n)=17*a(n), a(2n+1)=a(2n)+1.

0, 1, 17, 18, 289, 290, 306, 307, 4913, 4914, 4930, 4931, 5202, 5203, 5219, 5220, 83521, 83522, 83538, 83539, 83810, 83811, 83827, 83828, 88434, 88435, 88451, 88452, 88723, 88724, 88740, 88741, 1419857, 1419858, 1419874, 1419875

Offset: 0

Author

Philippe Deléham, Oct 14 2011

Keywords

• easy
• nonn
• base

Comments

Numbers whose set of base 17 digits is {0,1}.

Sums of distinct powers of 17.

a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - Philippe Deléham, Oct 17 2011.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• 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. A001026, A104257.

Programs

Magma

[n: n in [0..1500000] | Set(IntegerToSequence(n, 17)) subset {0, 1}]; // Vincenzo Librandi, Jun 05 2012

Mathematica

Take[Union[Total/@Subsets[17^Range[0,20],5]],40] (* Harvey P. Dale, Dec 17 2011 *)
FromDigits[#,17]&/@Tuples[{0,1},5] (* Vincenzo Librandi, Jun 05 2012 *)

Formula

a(n)=Sum_k>=0 {A030308(n,k)*17^k}.

G.f.: (1/(1 - x))*Sum_{k>=0} 17^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017