A292249 Compound filter (multiplicative order of 2 mod 2n+1 & prime signature of 2n+1): a(n) = P(A002326(n), A046523(2n+1)), where P(n,k) is sequence A000027 used as a pairing function.

1, 5, 14, 9, 42, 65, 90, 40, 44, 189, 61, 77, 273, 318, 434, 20, 115, 148, 702, 148, 230, 119, 265, 299, 297, 86, 1430, 320, 271, 1769, 1890, 142, 148, 2277, 373, 665, 54, 485, 625, 819, 2400, 3485, 86, 556, 77, 148, 115, 856, 1224, 850, 5150, 1377, 832, 5777, 702, 856, 434, 1220, 265, 430, 6438, 320, 5771, 35, 185, 8645, 271

Offset: 0

Author

Antti Karttunen, Oct 02 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000027, A002326, A046523, A278223, A286573, A291769 (rgs-version of the same filter).

Cf. also A291755, A292268.

Programs

PARI

A002326(n) = if(n<0, 0, znorder(Mod(2, 2*n+1))); \\ This function from Michael Somos, Mar 31 2005
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A292249(n) = (1/2)*(2 + ((A002326(n)+A046523(n+n+1))^2) - A002326(n) - 3*A046523(n+n+1));

Scheme

(define (A292249 n) (* 1/2 (+ (expt (+ (A002326 n) (A046523 (+ 1 n n))) 2) (- (A002326 n)) (- (* 3 (A046523 (+ 1 n n)))) 2)))

Formula

a(n) = (1/2)*(2 + ((A002326(n) + A046523(2n+1))^2) - A002326(n) - 3*A046523(2n+1)).