A221982 Primes p == 2 (mod 5) for which 4*p+1 is also prime.

7, 37, 67, 97, 127, 277, 307, 487, 577, 727, 997, 1087, 1297, 1327, 1567, 1597, 1777, 1987, 2017, 2437, 2647, 2677, 2767, 2887, 3037, 3067, 3307, 3457, 3637, 3907, 4057, 4297, 4447, 4567, 4987, 5197, 5527, 5557, 6007, 6247, 6337, 6367, 6397, 6547, 6577, 7027, 7057, 7237, 7417, 7507, 7717, 7867

Offset: 1

Author

Jonathan Sondow, Feb 02 2013

Keywords

• nonn

Comments

The corresponding primes 4*p+1 are Chebyshev's subsequence A221981 of the primes with primitive root 10.

Examples

			7 is a member because 7 == 2 (mod 5) and 29 = 4*7 + 1 are both prime.
		

References

• P. L. Chebyshev, Theory of congruences. Elements of number theory, Chelsea, 1972, p. 306.
• R. K. Guy, Unsolved Problems in Number Theory, F9.

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000
• P. Moree, Artin's primitive root conjecture - a survey, arXiv 2004, revised 2012, p. 1.
• Index entries for primes by primitive root

Crossrefs

Cf. A001913, A006883, A045380, A106849, A221981, A222008.

Programs

Maple

A221982:=proc(q)
local n;
for n from 1 to q do
if isprime(n) and isprime(4*n+1) and (n mod 5)=2 then print(n) fi; od; end:
A221982 (10000); # Paolo P. Lava, Feb 12 2013

Mathematica

Select[ Prime[ Range[1000]], Mod[#, 5] == 2 && PrimeQ[4 # + 1] &]

Formula

a(n) = (A221981(n) - 1)/4.