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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.
5
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
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)))
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 14 2017
STATUS
approved