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 A102563 #8 Jul 22 2023 17:34:52 %S A102563 0,0,0,1,1,2,2,1,3,4,4,3,5,4,4,3,7,8,8,7,9,8,8,7,11,10,10,9,11,10,10, %T A102563 5,15,16,16,15,17,16,16,15,19,18,18,17,19,18,18,13,23,22,22,21,23,22, %U A102563 22,17,25,24,24,19,25,20,20,11,31,32,32,31,33,32,32,31,35,34,34,33,35,34 %N A102563 a(n) = A000120(A001045(n)) - A001045(A000120(n)). %H A102563 Amiram Eldar, <a href="/A102563/b102563.txt">Table of n, a(n) for n = 0..10000</a> %F A102563 It would appear that a(2^(n+1)) = A000225(n). %F A102563 a(2^(n+1)-1) = A001045(n). %F A102563 a(2^(n+1)+1) = A000079(n). %F A102563 a(2n+1) = n; a(4n+1) - a(2n+1) = n; a(8n+1) - a(4n+1) = 2n; a(8n+1) - a(2n+1) = 3n. %t A102563 j[n_] := (2^n - (-1)^n)/3; s[n_] := DigitCount[n, 2, 1]; a[n_] := s[j[n]] - j[s[n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jul 22 2023 *) %Y A102563 Cf. A000079, A000120, A000225, A001045, A102564, 102565. %K A102563 easy,nonn,base %O A102563 0,6 %A A102563 _Paul Barry_, Jan 14 2005