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

0,2

Links

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

Formula

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

Prog

(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)))

Crossrefs

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

Cf. also A291755, A292268.

Sequence in context: A003079 A334119 A205128 * A205134 A196363 A169811

Adjacent sequences: A292246 A292247 A292248 * A292250 A292251 A292252

Keyword

nonn

Author

Antti Karttunen, Oct 02 2017

Status

approved