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

Author

Antti Karttunen, May 17 2017

Keywords

• nonn

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)

Crossrefs

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

Cf. A083668 (positions of 5's).

Programs

Scheme

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

Formula

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