A197353 a(0)=0, a(1)=1, a(2n)=19*a(n), a(2n+1)=a(2n)+1.

0, 1, 19, 20, 361, 362, 380, 381, 6859, 6860, 6878, 6879, 7220, 7221, 7239, 7240, 130321, 130322, 130340, 130341, 130682, 130683, 130701, 130702, 137180, 137181, 137199, 137200, 137541, 137542, 137560, 137561, 2476099, 2476100, 2476118, 2476119

Offset: 0

Author

Philippe Deléham, Oct 14 2011

Keywords

• easy
• nonn

Comments

Numbers whose set of base 19 digits is {0,1}.

Sums of distinct powers of 19.

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. A001029, A010060, A104257, A030308, A197352.

Programs

Magma

[n: n in [0..2500000] | Set(IntegerToSequence(n, 19)) subset {0, 1}]; // Vincenzo Librandi, Jun 05 2012

Mathematica

FromDigits[#,19]&/@Tuples[{0,1},5] (* Vincenzo Librandi, Jun 05 2012 *)

Formula

a(n) = Sum_{k>=0} A030308(n,k)*19^k.

G.f.: (1/(1 - x))*Sum_{k>=0} 19^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017