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

Author

Zak Seidov, Sep 25 2014

Keywords

• nonn

Comments

Both p and p + 2 are terms in A038878.

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

Examples

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

Links

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

Crossrefs

Cf. A001359, A038878.

Programs

Mathematica

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

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