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

1,1

Comments

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

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

Formula

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

Example

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

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] &]

Crossrefs

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

Sequence in context: A168003 A132231 A289353 * A104915 A089376 A337423

Adjacent sequences: A221979 A221980 A221981 * A221983 A221984 A221985

Keyword

nonn

Author

Jonathan Sondow, Feb 02 2013

Status

approved