A292268 Compound filter (multiplicative order of 2 mod 2n+1 & number of trailing 1's in binary expansion of 2n+1): a(n) = P(A002326(n), A007814(2n+2)), where P(n,k) is sequence A000027 used as a pairing function.

1, 5, 10, 13, 21, 65, 78, 25, 36, 189, 21, 89, 210, 189, 406, 41, 55, 90, 666, 103, 210, 119, 78, 348, 231, 44, 1378, 251, 171, 1769, 1830, 61, 78, 2277, 253, 701, 45, 230, 465, 900, 1485, 3485, 36, 463, 66, 90, 55, 816, 1176, 495, 5050, 1429, 78, 5777, 666, 777, 406, 1034, 78, 349, 6105, 230, 5050, 85, 105, 8645, 171, 739, 2346, 9729, 1081

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, A007814, A292267 (rgs-version of this filter).

Cf. also A291755, A292249.

Programs

PARI

A002326(n) = if(n<0, 0, znorder(Mod(2, 2*n+1))); \\ This function from Michael Somos, Mar 31 2005
A007814(n) = valuation(n,2);
A292268(n) = (1/2)*(2 + ((A002326(n)+A007814(2*(1+n)))^2) - A002326(n) - 3*A007814(2*(1+n)));

Scheme

(define (A292268 n) (* 1/2 (+ (expt (+ (A002326 n) (A007814 (+ 2 n n))) 2) (- (A002326 n)) (- (* 3 (A007814 (+ 2 n n)))) 2)))

Formula

a(n) = (1/2)*(2 + ((A002326(n) + A007814(2n+2))^2) - A002326(n) - 3*A007814(2n+2)).