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 A033044 #75 Oct 31 2022 02:09:06
%S A033044 0,1,7,8,49,50,56,57,343,344,350,351,392,393,399,400,2401,2402,2408,
%T A033044 2409,2450,2451,2457,2458,2744,2745,2751,2752,2793,2794,2800,2801,
%U A033044 16807,16808,16814,16815,16856,16857,16863,16864,17150,17151,17157
%N A033044 Sums of distinct powers of 7.
%C A033044 Numbers without any base-7 digits greater than 1.
%C A033044 a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - _Philippe Deléham_, Oct 17 2011
%C A033044 Note that this sequence has offset 1, in contrast to A000695 and all others among A033043-A033052. - _M. F. Hasler_, Feb 01 2016
%H A033044 T. D. Noe, <a href="/A033044/b033044.txt">Table of n, a(n) for n = 1..1024</a>
%H A033044 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 A033044 a(n) = Sum_{i=0..m} d(i)*7^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
%F A033044 a(n) = A097253(n)/6.
%F A033044 a(2n) = 7*a(n), a(2n+1) = a(2n)+1.
%F A033044 a(n+1) = Sum_{k>=0} A030308(n,k)*7^k. - _Philippe Deléham_, Oct 17 2011
%F A033044 G.f.: (x/(1 - x))*Sum_{k>=0} 7^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017
%t A033044 t = Table[FromDigits[RealDigits[n, 2], 7], {n, 0, 100}]
%t A033044 (* _Clark Kimberling_, Aug 03 2012 *)
%t A033044 FromDigits[#,7]&/@Tuples[{0,1},6] (* _Harvey P. Dale_, Apr 30 2015 *)
%o A033044 (PARI) A033044(n,b=7)=subst(Pol(binary(n-1)),'x,b) \\ _M. F. Hasler_, Feb 01 2016
%o A033044 (PARI) a(n)=fromdigits(binary(n), 7) \\ _Charles R Greathouse IV_, Jan 11 2017
%Y A033044 Cf. A000695, A005836, A033043-A033052, A037412.
%Y A033044 Row 7 of array A104257.
%K A033044 nonn,base,easy
%O A033044 1,3
%A A033044 _Clark Kimberling_
%E A033044 Extended by _Ray Chandler_, Aug 03 2004
%E A033044 _Karol Bacik_ has pointed out that the first three formulas do not match the sequence. - _N. J. A. Sloane_, Oct 20 2012