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 A330262 #11 Feb 27 2020 23:16:02 %S A330262 1,0,1,1,1,0,1,0,1,-1,1,1,1,0,1,1,1,0,1,2,1,0,1,0,1,-1,1,1,1,0,1,0,1, %T A330262 -1,1,-1,1,0,1,-1,1,-2,1,0,1,0,1,1,1,0,1,2,1,0,1,0,1,-1,1,1,1,0,1,1,1, %U A330262 -1,1,0,1,0,1,-3,1,-3,1,1,1,0,1,2,1,-2,1 %N A330262 Start with an empty stack S; for n = 1, 2, 3, ..., interpret the binary representation of n from left to right as follows: in case of bit 1, push the number 1 on top of S, in case of bit 0, replace the two numbers on top of S, say u on top of v, with v-u; a(n) gives the number on top of S after processing n. %C A330262 This sequence is a variant of A330261. %C A330262 After processing n, S has A268289(n) elements. %C A330262 Every integer appears infinitely many times in the sequence: %C A330262 - the proof is similar to that found in A330261, %C A330262 - see A330265 for the values in order of appearance. %H A330262 Rémy Sigrist, <a href="/A330262/b330262.txt">Table of n, a(n) for n = 1..8192</a> %H A330262 Rémy Sigrist, <a href="/A330262/a330262.png">Scatterplot of the first 2^20 terms</a> %H A330262 Rémy Sigrist, <a href="/A330262/a330262.gp.txt">PARI program for A330262</a> %e A330262 The first terms, alongside the binary representation of n and the evolution of stack S, are: %e A330262 n a(n) bin(n) S %e A330262 - ---- ------ ------------------------------------------------------------ %e A330262 1 1 1 () -> (1) %e A330262 2 0 10 (1) -> (1,1) -> (0) %e A330262 3 1 11 (0) -> (0,1) -> (0,1,1) %e A330262 4 1 100 (0,1,1) -> (0,1,1,1) -> (0,1,0) -> (0,1) %e A330262 5 1 101 (0,1) -> (0,1,1) -> (0,0) -> (0,0,1) %e A330262 6 0 110 (0,0,1) -> (0,0,1,1) -> (0,0,1,1,1) -> (0,0,1,0) %e A330262 7 1 111 (0,0,1,0) -> (0,0,1,0,1) -> (0,0,1,0,1,1) -> (0,0,1,0,1,1,1) %o A330262 (PARI) See Links section. %Y A330262 Cf. A268289, A308551, A330261, A330265. %K A330262 sign,base %O A330262 1,20 %A A330262 _Rémy Sigrist_, Dec 07 2019