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

%I A197353 #32 Oct 24 2024 03:12:27
%S A197353 0,1,19,20,361,362,380,381,6859,6860,6878,6879,7220,7221,7239,7240,
%T A197353 130321,130322,130340,130341,130682,130683,130701,130702,137180,
%U A197353 137181,137199,137200,137541,137542,137560,137561,2476099,2476100,2476118,2476119
%N A197353 a(0)=0, a(1)=1, a(2n)=19*a(n), a(2n+1)=a(2n)+1.
%C A197353 Numbers whose set of base 19 digits is {0,1}.
%C A197353 Sums of distinct powers of 19.
%C A197353 a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - _Philippe Deléham_, Oct 17 2011
%H A197353 Vincenzo Librandi, <a href="/A197353/b197353.txt">Table of n, a(n) for n = 0..1000</a>
%H A197353 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 A197353 a(n) = Sum_{k>=0} A030308(n,k)*19^k.
%F A197353 G.f.: (1/(1 - x))*Sum_{k>=0} 19^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%t A197353 FromDigits[#,19]&/@Tuples[{0,1},5] (* _Vincenzo Librandi_, Jun 05 2012 *)
%o A197353 (Magma) [n: n in [0..2500000] | Set(IntegerToSequence(n, 19)) subset {0, 1}]; // _Vincenzo Librandi_, Jun 05 2012
%Y A197353 Cf. A001029, A010060, A104257, A030308, A197352.
%K A197353 easy,nonn
%O A197353 0,3
%A A197353 _Philippe Deléham_, Oct 14 2011