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 A118551 #12 Mar 06 2024 04:49:13
%S A118551 1,2,4,5,10,20,21,22,23,24,48,49,50,51,52,53,54,55,56,57,114,228,456,
%T A118551 912,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,
%U A118551 1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,3694,7388,14776
%N A118551 a(0)=1. a(n) = a(n-1)*2, if n is in the sequence. a(n) = a(n-1) + 1 if n is missing from the sequence.
%t A118551 f[s_] := Block[{n = Length@s}, Append[s, If[ MemberQ[s, n], 2s[[ -1]], s[[ -1]] + 1]]]; Nest[f, {1}, 50] (* _Robert G. Wilson v_, May 16 2006 *)
%K A118551 easy,nonn
%O A118551 0,2
%A A118551 _Leroy Quet_, May 03 2006
%E A118551 More terms from _Robert G. Wilson v_, May 16 2006