A293429 a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n-1) - A008966(4n+1)).

0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 3, 3, 3, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 3, 4, 4, 4, 3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 2, 2, 3, 3, 4, 4, 4, 4, 4, 3, 3, 4, 4, 5, 5, 5, 4, 4, 3, 3, 4, 3, 4, 4, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3

Offset

0,7

Comments

The sequence indicates about a possible bias (or lack of it) in the distribution of squarefree numbers among the numbers of the form 4k-1 vs. the numbers of the form 4k+1. See A293229 for another version.

The first negative term is a(4014) = -1.

Links

Antti Karttunen, Table of n, a(n) for n = 0..11111

Hans Havermann, Plot of n, a(n) for n = 0..200000

Formula

a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n-1) - A008966(4n+1)).

Prog

(Scheme, with memoization-macro definec)
(definec (A293429 n) (if (zero? n) n (+ (- (A008966 (+ -1 (* 4 n))) (A008966 (+ 1 (* 4 n)))) (A293429 (- n 1)))))

Crossrefs

Cf. A008966, A293229 (a variant).

Sequence in context: A094102 A220091 A063746 * A367313 A201075 A131338

Adjacent sequences: A293426 A293427 A293428 * A293430 A293431 A293432

Keyword

sign

Author

Antti Karttunen, Oct 16 2017

Status

approved