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

1,2

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

Formula

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

Prog

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

Crossrefs

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

Sequence in context: A229469 A314574 A314575 * A293913 A213881 A179832

Adjacent sequences: A286451 A286452 A286453 * A286455 A286456 A286457

Keyword

nonn

Author

Antti Karttunen, May 14 2017

Status

approved