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

%I A197351 #34 Oct 28 2022 08:51:28
%S A197351 0,1,17,18,289,290,306,307,4913,4914,4930,4931,5202,5203,5219,5220,
%T A197351 83521,83522,83538,83539,83810,83811,83827,83828,88434,88435,88451,
%U A197351 88452,88723,88724,88740,88741,1419857,1419858,1419874,1419875
%N A197351 a(0)=0, a(1)=1, a(2n)=17*a(n), a(2n+1)=a(2n)+1.
%C A197351 Numbers whose set of base 17 digits is {0,1}.
%C A197351 Sums of distinct powers of 17.
%C A197351 a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - _Philippe Deléham_, Oct 17 2011.
%H A197351 Vincenzo Librandi, <a href="/A197351/b197351.txt">Table of n, a(n) for n = 0..1000</a>
%H A197351 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 A197351 a(n)=Sum_k>=0 {A030308(n,k)*17^k}.
%F A197351 G.f.: (1/(1 - x))*Sum_{k>=0} 17^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%t A197351 Take[Union[Total/@Subsets[17^Range[0,20],5]],40] (* _Harvey P. Dale_, Dec 17 2011 *)
%t A197351 FromDigits[#,17]&/@Tuples[{0,1},5] (* _Vincenzo Librandi_, Jun 05 2012 *)
%o A197351 (Magma) [n: n in [0..1500000] | Set(IntegerToSequence(n, 17)) subset {0, 1}]; // _Vincenzo Librandi_, Jun 05 2012
%Y A197351 Cf. A001026, A104257.
%K A197351 easy,nonn,base
%O A197351 0,3
%A A197351 _Philippe Deléham_, Oct 14 2011