A286454 Compound filter (prime signature & prime signature of conjugated prime factorization): a(n) = P(A101296(n), A286621(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 5, 8, 9, 12, 32, 23, 20, 13, 49, 38, 51, 47, 82, 49, 35, 68, 51, 80, 72, 124, 140, 122, 74, 18, 175, 26, 111, 155, 334, 192, 65, 257, 280, 82, 116, 255, 329, 355, 99, 327, 570, 380, 177, 72, 469, 437, 132, 31, 72, 532, 216, 498, 74, 257, 144, 599, 634, 597, 448, 632, 745, 159, 119, 784, 1044, 782, 331, 907, 570, 863, 186, 905, 1039, 72, 384, 140, 1335, 1037

Offset: 1

Author

Antti Karttunen, May 14 2017

Keywords

• nonn

Comments

Here, instead of A046523 and A278221 we use as the components of a(n) their rgs-versions A101296 and A286621 because of the latter sequence's moderate growth rates.

For all i, j: a(i) = a(j) => A286356(i) = A286356(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pairing Function

Crossrefs

Cf. A000027, A046523, A101296, A122111, A278221, A285334, A286621, A286356, A286455, A286456.

Programs

Scheme

(define (A286454 n) (* (/ 1 2) (+ (expt (+ (A101296 n) (A286621 n)) 2) (- (A101296 n)) (- (* 3 (A286621 n))) 2)))

Formula

a(n) = (1/2)*(2 + ((A101296(n)+A286621(n))^2) - A101296(n) - 3*A286621(n)).