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%I #38 Oct 31 2022 02:10:08
%S 0,1,15,16,225,226,240,241,3375,3376,3390,3391,3600,3601,3615,3616,
%T 50625,50626,50640,50641,50850,50851,50865,50866,54000,54001,54015,
%U 54016,54225,54226,54240,54241,759375,759376,759390,759391,759600
%N Numbers whose set of base 15 digits is {0,1}.
%C Sums of distinct powers of 15.
%C a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - _Philippe Deléham_, Oct 17 2011.
%H T. D. Noe, <a href="/A033051/b033051.txt">Table of n, a(n) for n = 0..1023</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_{i=0..m} d(i)*15^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
%F a(n) = A097261(n)/14.
%F a(2n) = 15*a(n), a(2n+1) = a(2n)+1.
%F a(n) = Sum_{k>=0} A030308(n,k)*15^k. - _Philippe Deléham_, Oct 17 2011.
%F G.f.: (1/(1 - x))*Sum_{k>=0} 15^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%t With[{k = 15}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* _Michael De Vlieger_, Oct 28 2022 *)
%o (PARI) A033051(n, b=15)=subst(Pol(binary(n)),'x,b) \\ _M. F. Hasler_, Feb 01 2016
%Y Cf. A000695, A005836, A033042-A033052.
%Y Row 14 of array A104257.
%K nonn,base,easy
%O 0,3
%A _Clark Kimberling_
%E Extended by _Ray Chandler_, Aug 03 2004
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