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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.
4
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 02 2017
STATUS
approved