A216366 Lesser of pairs of odd numbers (n, n+2) such that the product of invertible quadratic residues == (n+1)(-1)^((n+1)/2) (modulo n(n+2)).

1, 3, 5, 11, 17, 23, 25, 27, 29, 41, 59, 61, 71, 97, 99, 101, 107, 125, 137, 147, 149, 167, 169, 171, 179, 191, 197, 227, 229, 231, 239, 241, 269, 277, 279, 281, 311, 347, 387, 397, 399, 419, 421, 431, 461, 521, 539, 567, 569, 599, 601, 617, 625, 639, 641

Offset

1,2

Comments

Twin primes satisfy the same property, so A001359 is included in this sequence.

Links

Table of n, a(n) for n=1..55.

Christian Aebi and Grant Cairns, A property of twin primes, Integers 12(2012), A7.

Prog

(PARI) isptp (p) = {local(pq); pq = p*(p+2); if (prod(x=1, pq, if (issquare(Mod(x, pq)) && (gcd(x, pq) == 1), x, 1)) % pq == ((p+1) * ((-1)^((p+1)/2))) % pq , return(1), return(0)); } allptp(n) = {local(i, p, q); p = []; q = []; forstep (i=1, n, 2, if (isptp(i), p = concat(p, i); q = concat(q, i+2); ); ); print(p); print(q); }

Crossrefs

Cf. A001359, A006512, A001097.

Sequence in context: A050566 A032382 A167921 * A136084 A045410 A248173

Adjacent sequences: A216363 A216364 A216365 * A216367 A216368 A216369

Keyword

nonn

Author

Michel Marcus, Sep 05 2012

Status

approved