A286467 Compound filter (prime signature of n & prime signature of the n-th Fibonacci number): a(n) = P(A101296(n), A286545(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 3, 5, 9, 5, 19, 5, 33, 18, 25, 5, 51, 5, 25, 40, 73, 5, 72, 12, 84, 40, 25, 5, 128, 69, 25, 71, 84, 5, 180, 12, 146, 40, 25, 40, 242, 23, 40, 40, 198, 12, 180, 5, 177, 177, 40, 5, 337, 31, 216, 40, 84, 12, 284, 59, 308, 140, 40, 12, 478, 12, 40, 177, 339, 40, 180, 23, 177, 140, 387, 12, 610, 12, 59, 216, 177, 59, 309, 12, 540, 332, 40, 5, 608, 59, 40, 59

Offset

1,2

Comments

Nonsquare semiprimes pq for which F(pq) is also a semiprime is given by the positions where 25's occur in this sequence: 10, 14, 22, 26, 34, 94, (any more terms?). This is a subsequence of A072381.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1300 (based also on the b-file of A278245 provided by Hans Havermann)

Formula

a(n) = (1/2)*(2 + ((A101296(n) + A286545(n))^2) - A101296(n) - 3*A286545(n)).

Prog

(Scheme) (define (A286467 n) (* (/ 1 2) (+ (expt (+ (A101296 n) (A286545 n)) 2) (- (A101296 n)) (- (* 3 (A286545 n))) 2)))

Crossrefs

Cf. A000027, A046523, A072381, A101296, A278245, A286545.

Cf. A083668 (positions of 5's).

Sequence in context: A076844 A198558 A286566 * A231736 A212437 A048639

Adjacent sequences: A286464 A286465 A286466 * A286468 A286469 A286470

Keyword

nonn

Author

Antti Karttunen, May 17 2017

Status

approved