A197352 a(0)=0, a(1)=1, a(2n)=18*a(n), a(2n+1)=a(2n)+1.

0, 1, 18, 19, 324, 325, 342, 343, 5832, 5833, 5850, 5851, 6156, 6157, 6174, 6175, 104976, 104977, 104994, 104995, 105300, 105301, 105318, 105319, 110808, 110809, 110826, 110827, 111132, 111133, 111150, 111151, 1889568, 1889569, 1889586, 1889587

Offset: 0

Author

Philippe Deléham, Oct 14 2011

Keywords

• easy
• nonn
• base

Comments

Numbers whose set of base 18 digits is {0,1}.

Sums of distinct powers of 18.

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. A001027, A104257, A197351.

Programs

Magma

[n: n in [0..2000000] | Set(IntegerToSequence(n, 18)) subset {0, 1}]; // Vincenzo Librandi, Jun 05 2012

Mathematica

FromDigits[#,18]&/@Tuples[{0,1},5] (* Vincenzo Librandi, Jun 05 2012 *)

Formula

a(n) = Sum_{k>=0} A030308(n,k)*18^k.

G.f.: (1/(1 - x))*Sum_{k>=0} 18^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017