cp's OEIS Frontend

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

%I A197352 #26 Oct 31 2022 02:05:50
%S A197352 0,1,18,19,324,325,342,343,5832,5833,5850,5851,6156,6157,6174,6175,
%T A197352 104976,104977,104994,104995,105300,105301,105318,105319,110808,
%U A197352 110809,110826,110827,111132,111133,111150,111151,1889568,1889569,1889586,1889587
%N A197352 a(0)=0, a(1)=1, a(2n)=18*a(n), a(2n+1)=a(2n)+1.
%C A197352 Numbers whose set of base 18 digits is {0,1}.
%C A197352 Sums of distinct powers of 18.
%H A197352 Vincenzo Librandi, <a href="/A197352/b197352.txt">Table of n, a(n) for n = 0..1000</a>
%H A197352 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 A197352 a(n) = Sum_{k>=0} A030308(n,k)*18^k.
%F A197352 G.f.: (1/(1 - x))*Sum_{k>=0} 18^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%t A197352 FromDigits[#,18]&/@Tuples[{0,1},5] (* _Vincenzo Librandi_, Jun 05 2012 *)
%o A197352 (Magma) [n: n in [0..2000000] | Set(IntegerToSequence(n, 18)) subset {0, 1}]; // _Vincenzo Librandi_, Jun 05 2012
%Y A197352 Cf. A001027, A104257, A197351.
%K A197352 easy,nonn,base
%O A197352 0,3
%A A197352 _Philippe Deléham_, Oct 14 2011