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 A292378 #10 Sep 18 2017 09:26:04 %S A292378 0,0,1,0,0,1,1,0,-1,0,2,1,1,1,2,0,0,-1,1,0,-1,2,2,1,-2,1,1,1,1,2,2,0, %T A292378 0,0,3,-1,1,1,3,0,0,-1,1,2,0,2,2,1,-3,-2,2,1,1,1,0,1,-1,1,2,2,1,2,1,0, %U A292378 -1,0,2,0,0,3,3,-1,2,1,0,1,2,3,3,0,-1,0,4,-1,2,1,3,2,3,0,1,2,0,2,3,1,2,-3,2,-2,1,2,2,1,1 %N A292378 a(n) = 1 + A292377(n) - A292375(n). %C A292378 Locate the node which contains n in binary tree A005940 and traverse towards the root (which is 1), counting separately all numbers of the form 4k+1 and of the form 4k+3 that occur on the path (including also starting n itself, if it is of the either form), until 1 is reached, which however, is never included in the count of 4k+1. a(n) is the count of 4k+3 numbers minus the count of 4k+1 numbers that were encountered. %H A292378 Antti Karttunen, <a href="/A292378/b292378.txt">Table of n, a(n) for n = 1..16384</a> %H A292378 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a> %F A292378 a(n) = 1 + (A292377(n) - A292375(n)). %F A292378 a(A000040(n)) = A038698(n). %t A292378 a[1, 1] = 1; a[1, 3] = 0; a[n_, k_] := a[n, k] = a[Which[n == 1, 1, EvenQ@ n, n/2, True, Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n], k] + Boole[Mod[n, 4] == k]; Array[a[#, 3] - a[#, 1] &, 105] (* _Michael De Vlieger_, Sep 17 2017 *) %o A292378 (Scheme) (define (A292378 n) (+ 1 (- (A292377 n) (A292375 n)))) %Y A292378 Cf. A000040, A038698, A292375, A292377. %K A292378 sign %O A292378 1,11 %A A292378 _Antti Karttunen_, Sep 17 2017