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 A308551 #22 Feb 27 2020 23:23:10 %S A308551 1,2,1,3,1,2,1,4,1,3,1,3,1,2,1,5,1,12,1,4,1,2,1,4,1,3,1,3,1,2,1,6,1, %T A308551 15,1,23,1,2,1,5,1,4,1,4,1,2,1,5,1,4,1,4,1,2,1,4,1,3,1,3,1,2,1,7,1,19, %U A308551 1,30,1,2,1,47,1,57,1,5,1,2,1,6,1,20,1,5 %N A308551 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 with their sum; a(n) gives the number on top of S after processing n. %C A308551 After processing n, S has A268289(n) elements, the sum of which is A000788(n). %C A308551 Every positive integer appears infinitely many times in the sequence. %C A308551 The sequence has the same shape when represented at different scales. %H A308551 Rémy Sigrist, <a href="/A308551/b308551.txt">Table of n, a(n) for n = 1..8192</a> %H A308551 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a308/A308551.java">Java program</a> (github) %H A308551 Rémy Sigrist, <a href="/A308551/a308551.gp.txt">PARI program</a> %H A308551 Wikipedia, <a href="https://en.wikipedia.org/wiki/Stack_(abstract_data_type)">Stack (abstract data type)</a> %F A308551 a(n) = 1 iff n is odd. %F A308551 a(A020989(k)) = k + 1 for any k >= 0. %F A308551 If n is in A014486, then a(n) = a(n-1) + A000120(n) = 1 + A000120(n). - _Charlie Neder_, Jun 07 2019 %e A308551 The first terms, alongside the binary representation of n and the evolution of stack S, are: %e A308551 n a(n) bin(n) S %e A308551 - ---- ------ ------------------------------------------------- %e A308551 1 1 1 () -> (1) %e A308551 2 2 10 (1) -> (1,1) -> (2) %e A308551 3 1 11 (2) -> (2,1) -> (2,1,1) %e A308551 4 3 100 (2,1,1) -> (2,1,1,1) -> (2,1,2) -> (2,3) %e A308551 5 1 101 (2,3) -> (2,3,1) -> (2,4) -> (2,4,1) %e A308551 6 2 110 (2,4,1) -> (2,4,1,1) -> (2,4,1,1,1) -> (2,4,1,2) %o A308551 (Java) See Links section. %o A308551 (PARI) See Links section. %Y A308551 Cf. A000788, A020989, A268289. %K A308551 nonn,base,look %O A308551 1,2 %A A308551 _Rémy Sigrist_, Jun 07 2019