A197352 - OEIS

%I #26 Oct 31 2022 02:05:50

%S 0,1,18,19,324,325,342,343,5832,5833,5850,5851,6156,6157,6174,6175,

%T 104976,104977,104994,104995,105300,105301,105318,105319,110808,

%U 110809,110826,110827,111132,111133,111150,111151,1889568,1889569,1889586,1889587

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

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

%C Sums of distinct powers of 18.

%H Vincenzo Librandi, <a href="/A197352/b197352.txt">Table of n, a(n) for n = 0..1000</a>

%H Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, p. 45.

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

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

%t FromDigits[#,18]&/@Tuples[{0,1},5] (* _Vincenzo Librandi_, Jun 05 2012 *)

%o (Magma) [n: n in [0..2000000] | Set(IntegerToSequence(n, 18)) subset {0, 1}]; // _Vincenzo Librandi_, Jun 05 2012

%Y Cf. A001027, A104257, A197351.

%K easy,nonn,base

%O 0,3

%A _Philippe Deléham_, Oct 14 2011