This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A033051 #40 Sep 15 2024 19:46:52
%S A033051 0,1,15,16,225,226,240,241,3375,3376,3390,3391,3600,3601,3615,3616,
%T A033051 50625,50626,50640,50641,50850,50851,50865,50866,54000,54001,54015,
%U A033051 54016,54225,54226,54240,54241,759375,759376,759390,759391,759600
%N A033051 Numbers whose set of base 15 digits is {0,1}.
%C A033051 Sums of distinct powers of 15.
%C A033051 a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - _Philippe Deléham_, Oct 17 2011.
%H A033051 T. D. Noe, <a href="/A033051/b033051.txt">Table of n, a(n) for n = 0..1023</a>
%H A033051 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 A033051 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 A033051 a(n) = A097261(n)/14.
%F A033051 a(2n) = 15*a(n), a(2n+1) = a(2n)+1.
%F A033051 a(n) = Sum_{k>=0} A030308(n,k)*15^k. - _Philippe Deléham_, Oct 17 2011.
%F A033051 G.f.: (1/(1 - x))*Sum_{k>=0} 15^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%t A033051 With[{k = 15}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* _Michael De Vlieger_, Oct 28 2022 *)
%t A033051 FromDigits[#,15]&/@Tuples[{0,1},6] (* _Harvey P. Dale_, Sep 15 2024 *)
%o A033051 (PARI) A033051(n, b=15)=subst(Pol(binary(n)),'x,b) \\ _M. F. Hasler_, Feb 01 2016
%Y A033051 Cf. A000695, A005836, A033042-A033052.
%Y A033051 Row 14 of array A104257.
%K A033051 nonn,base,easy
%O A033051 0,3
%A A033051 _Clark Kimberling_
%E A033051 Extended by _Ray Chandler_, Aug 03 2004