A292378 a(n) = 1 + A292377(n) - A292375(n).

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, 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, -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

Offset: 1

Author

Antti Karttunen, Sep 17 2017

Keywords

• sign

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000040, A038698, A292375, A292377.

Programs

Mathematica

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 *)

Scheme

(define (A292378 n) (+ 1 (- (A292377 n) (A292375 n))))

Formula

a(n) = 1 + (A292377(n) - A292375(n)).

a(A000040(n)) = A038698(n).