cp's OEIS Frontend

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

%I A221982 #23 Feb 12 2013 11:54:24
%S A221982 7,37,67,97,127,277,307,487,577,727,997,1087,1297,1327,1567,1597,1777,
%T A221982 1987,2017,2437,2647,2677,2767,2887,3037,3067,3307,3457,3637,3907,
%U A221982 4057,4297,4447,4567,4987,5197,5527,5557,6007,6247,6337,6367,6397,6547,6577,7027,7057,7237,7417,7507,7717,7867
%N A221982 Primes p == 2 (mod 5) for which 4*p+1 is also prime.
%C A221982 The corresponding primes 4*p+1 are Chebyshev's subsequence A221981 of the primes with primitive root 10.
%D A221982 P. L. Chebyshev, Theory of congruences. Elements of number theory, Chelsea, 1972, p. 306.
%D A221982 R. K. Guy, Unsolved Problems in Number Theory, F9.
%H A221982 Paolo P. Lava, <a href="/A221982/b221982.txt">Table of n, a(n) for n = 1..10000</a>
%H A221982 P. Moree, <a href="http://arxiv.org/abs/math/0412262v2">Artin's primitive root conjecture - a survey</a>, arXiv 2004, revised 2012, p. 1.
%H A221982 <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
%F A221982 a(n) = (A221981(n) - 1)/4.
%e A221982 7 is a member because 7 == 2 (mod 5) and 29 = 4*7 + 1 are both prime.
%p A221982 A221982:=proc(q)
%p A221982 local n;
%p A221982 for n from 1 to q do
%p A221982 if isprime(n) and isprime(4*n+1) and (n mod 5)=2 then print(n) fi; od; end:
%p A221982 A221982 (10000); # _Paolo P. Lava_, Feb 12 2013
%t A221982 Select[ Prime[ Range[1000]], Mod[#, 5] == 2 && PrimeQ[4 # + 1] &]
%Y A221982 Cf. A001913, A006883, A045380, A106849, A221981, A222008.
%K A221982 nonn
%O A221982 1,1
%A A221982 _Jonathan Sondow_, Feb 02 2013