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

0,5

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

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)).

Prog

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

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).

Sequence in context: A326269 A052989 A358823 * A287274 A305099 A292141

Adjacent sequences: A252747 A252748 A252749 * A252751 A252752 A252753

Keyword

sign,tabf

Author

Antti Karttunen, Dec 21 2014

Extensions

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

Status

approved