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 A033045 #52 Oct 31 2022 02:09:15
%S A033045 0,1,8,9,64,65,72,73,512,513,520,521,576,577,584,585,4096,4097,4104,
%T A033045 4105,4160,4161,4168,4169,4608,4609,4616,4617,4672,4673,4680,4681,
%U A033045 32768,32769,32776,32777,32832,32833,32840,32841,33280,33281,33288
%N A033045 Sums of distinct powers of 8.
%C A033045 Numbers without any base-8 digits greater than 1.
%C A033045 Every nonnegative n is a unique sum of the form a(p)+2a(q)+4a(r). This gives a one-to-one map of the set N_0 of all nonnegative integers to (N_0)^3. Furthermore, if, for a fixed positive integer m, to consider all sums of distinct powers of 2^m, then one can obtain a one-to-one map of the set N_0 to (N_0)^m. - _Vladimir Shevelev_, Nov 15 2008
%H A033045 David A. Corneth, <a href="/A033045/b033045.txt">Table of n, a(n) for n = 0..9999</a> (first 1024 terms from T. D. Noe)
%H A033045 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.
%H A033045 Michael Penn, <a href="https://www.youtube.com/watch?v=e-Q_PpfC9do">"almost" a generating function...</a>, YouTube video, 2020.
%F A033045 a(n) = Sum_{i=0..m} d(i)*8^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
%F A033045 a(n) = A097254(n)/7.
%F A033045 a(2n) = 8*a(n), a(2n+1) = a(2n)+1.
%F A033045 a(n) = Sum_{k>=0} A030308(n,k)*8^k. - _Philippe Deléham_, Oct 19 2011
%F A033045 G.f.: (1/(1 - x))*Sum_{k>=0} 8^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%e A033045 a(7)=72 because 72_10 = 110_8.
%o A033045 (PARI) A033045(n,b=8)=subst(Pol(binary(n)),'x,b) \\ _M. F. Hasler_, Feb 01 2016
%o A033045 (PARI) a(n) = fromdigits(binary(n), 8) \\ _David A. Corneth_, Dec 17 2020
%Y A033045 Cf. A000695, A005836, A033043-A033052.
%Y A033045 Row 8 of array A104257.
%K A033045 nonn,base,easy
%O A033045 0,3
%A A033045 _Clark Kimberling_
%E A033045 More terms from _Patrick De Geest_, Dec 23 2000