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 A336533 #67 Oct 02 2020 11:55:26
%S A336533 1,2,3,5,6,7,10,11,13,14,15,23,26,27,29,30,31,47,55,58,59,61,62,63,93,
%T A336533 94,95,111,119,122,123,125,126,127,191,221,222,223,239,247,250,251,
%U A336533 253,254,255,382,383,447,477,478,479,495,503,506,507,509,510,511,767
%N A336533 Lexicographically earliest sequence of positive terms such that for any n > 0, n = Sum_{k >= 0} b(k)*a(k+1) where Sum_{k >= 0} b(k)*2^k is the binary expansion of a(n).
%C A336533 In other words, the binary expansion of the n-th term encodes a partition of n into distinct terms of the sequence.
%C A336533 This sequence is complete (as any integer can be written as a sum of distinct terms of this sequence).
%H A336533 Rémy Sigrist, <a href="/A336533/b336533.txt">Table of n, a(n) for n = 1..10000</a>
%H A336533 Rémy Sigrist, <a href="/A336533/a336533.png">Binary plot of the first 1000 terms</a>
%H A336533 Rémy Sigrist, <a href="/A336533/a336533.gp.txt">PARI program for A336533</a>
%H A336533 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A336533 a(Sum_{k = 1..n} a(k)) = 2^n - 1 for any n > 0.
%e A336533 The first terms, alongside their binary representation and the corresponding partition of n, are:
%e A336533 n a(n) bin(a(n)) Partition of n
%e A336533 -- ---- --------- -------------------------
%e A336533 1 1 1 a(1)
%e A336533 2 2 10 a(2)
%e A336533 3 3 11 a(2) + a(1)
%e A336533 4 5 101 a(3) + a(1)
%e A336533 5 6 110 a(3) + a(2)
%e A336533 6 7 111 a(3) + a(2) + a(1)
%e A336533 7 10 1010 a(4) + a(2)
%e A336533 8 11 1011 a(4) + a(2) + a(1)
%e A336533 9 13 1101 a(4) + a(3) + a(1)
%e A336533 10 14 1110 a(4) + a(3) + a(2)
%e A336533 11 15 1111 a(4) + a(3) + a(2) + a(1)
%o A336533 (PARI) See Links section.
%Y A336533 Cf. A029931, A133457.
%K A336533 nonn,base
%O A336533 1,2
%A A336533 _Rémy Sigrist_, Sep 26 2020