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 A344184 #12 May 14 2021 02:57:09 %S A344184 1,2,6,12,44,44,92,184,1208,1336,5304,5304,10680,10680,21368,42736, %T A344184 567024,673520,5383920,5383920,21535472,172283632,172283632,172283632, %U A344184 344774384,344774384,344774384,344774384,689559280,689559280,1379118576,2758237152,71477713888 %N A344184 Lexicographically earliest sequence of positive integers such that for any n > 0, the binary expansion of a(n) contains the binary expansion of k for k = 1..n and the binary expansion of a(n+1) is obtained by replacing a possibly empty substring of the binary expansion of a(n) by the binary expansion of n+1. %C A344184 This sequence is a variant of A056744, easier to compute. %C A344184 This sequence is not weakly increasing; a(109) < a(108). %H A344184 Rémy Sigrist, <a href="/A344184/b344184.txt">Table of n, a(n) for n = 1..1024</a> %H A344184 Rémy Sigrist, <a href="/A344184/a344184.png">Binary plot of the first 1024 terms</a> %H A344184 Rémy Sigrist, <a href="/A344184/a344184.gp.txt">PARI program for A344184</a> %F A344184 A144016(a(n)) >= n. %e A344184 The first terms, alongside their binary expansion, are: %e A344184 n a(n) bin(n) bin(a(n)) %e A344184 -- ----- ------ --------------- %e A344184 1 1 1 1 %e A344184 2 2 10 10 %e A344184 3 6 11 110 %e A344184 4 12 100 1100 %e A344184 5 44 101 101100 %e A344184 6 44 110 101100 %e A344184 7 92 111 1011100 %e A344184 8 184 1000 10111000 %e A344184 9 1208 1001 10010111000 %e A344184 10 1336 1010 10100111000 %e A344184 11 5304 1011 1010010111000 %e A344184 12 5304 1100 1010010111000 %e A344184 13 10680 1101 10100110111000 %e A344184 14 10680 1110 10100110111000 %e A344184 15 21368 1111 101001101111000 %o A344184 (PARI) See Links section. %Y A344184 Cf. A056744, A144016, A344183. %K A344184 nonn,base %O A344184 1,2 %A A344184 _Rémy Sigrist_, May 11 2021