A252750 a(n) = A003961(A005940(n+1)) - 2 * A005940(n+1).

-1, -1, -1, 1, -3, 3, 7, 11, -3, 1, 5, 21, -1, 39, 71, 49, -9, 5, 13, 23, 7, 45, 85, 87, 23, 47, 95, 153, 93, 267, 463, 179, -9, -5, -1, 43, -19, 81, 149, 109, -11, 91, 175, 195, 189, 345, 605, 309, -73, 167, 311, 241, 357, 435, 775, 531, 645, 529, 965, 909, 1151, 1551, 2639, 601, -15, -1, 7, 29, -11, 63, 127, 185, 5, 53, 125, 327, 87, 573, 997, 407, -65, 121, 253, 413, 231

Offset: 0

Author

Antti Karttunen, Dec 21 2014

Keywords

• sign
• tabf

Comments

From Antti Karttunen, May 21 2024: (Start)

Like A005940 itself, also this irregular table derived from it can be represented as a binary tree:

-1

|

................. -1 ..................

-1 1

-3 ......./ \....... 3 7 ......./ \....... 11

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

-3 1 5 21 -1 39 71 49

-9 5 13 23 7 45 85 87 23 47 95 153 93 267 463 179

etc.

(End)

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383

Crossrefs

Cf. A252743 (characteristic function for positive terms), A252751 (partial sums of sequence b(0) = 0, b(n) = a(n), for n>0).

Cf. A003961, A005940, A252745, A252748, A249820, A246282.

Cf. A062234 (when negated forms the left edge apart from the initial term), A003063 (right edge).

Cf. also A372562 (apart from the initial term, same data in square array).

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A252750(n) = (A003961(A005940(1+n)) - (2 * A005940(1+n))); \\ Antti Karttunen, May 21 2024

Scheme

(define (A252750 n) (- (A003961 (A005940 (+ 1 n))) (* 2 (A005940 (+ 1 n)))))

Formula

a(n) = A003961(A005940(n+1)) - 2 * A005940(n+1).

a(n) = A252748(A005940(n+1)).

Other identities. For all n >= 1:

sgn(a(n)) = (-1)^(1+A252743(n)).

Extensions

Term a(0) = -1 prepended by Antti Karttunen, May 21 2024