A247874 Lesser of twin primes (p, q=p+2) such that 7 is a square mod p and mod q.

29, 137, 197, 281, 419, 617, 641, 809, 1061, 1091, 1229, 1289, 1427, 1481, 1877, 1931, 2129, 2237, 2267, 2381, 2549, 2657, 2687, 2801, 2969, 3329, 3359, 3389, 3527, 3557, 3581, 3917, 4001, 4229, 4337, 4421, 4481, 4649, 4787, 5009, 5657, 5741, 5849, 5879, 6131, 6269, 6299, 6551, 6689, 7307

Offset

1,1

Comments

Both p and p + 2 are terms in A038878.

All terms are congruent to {1, 25, 27} mod 28.

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

7+29*1=36=6^2 and 7+31*3=100=10^2 hence 7 is a square mod 29 and mod 31.

Mathematica

Select[Prime[Range[5, 1000]], PrimeQ[# + 2] && JacobiSymbol[7, #] == JacobiSymbol[7, # + 2] == 1 &]

Prog

(PARI) lista(nn) = {forprime(p=2, nn, if (isprime(q=p+2) && issquare(Mod(7, p)) && issquare(Mod(7, q)), print1(p, ", ")); ); } \\ Michel Marcus, Sep 25 2014

Crossrefs

Cf. A001359, A038878.

Sequence in context: A260260 A067985 A118873 * A162834 A145980 A142622

Adjacent sequences: A247871 A247872 A247873 * A247875 A247876 A247877

Keyword

nonn

Author

Zak Seidov, Sep 25 2014

Status

approved