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

0,2

Links

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

Formula

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

Prog

(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)))

Crossrefs

Cf. A000027, A002326, A007814, A292267 (rgs-version of this filter).

Cf. also A291755, A292249.

Sequence in context: A313448 A313449 A313450 * A309593 A272267 A195735

Adjacent sequences: A292265 A292266 A292267 * A292269 A292270 A292271

Keyword

nonn

Author

Antti Karttunen, Oct 02 2017

Status

approved