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%I M1406 #68 Sep 12 2022 07:59:10
%S 2,5,11,41,89,179,359,509,719,1019,1031,1229,1409,1451,1481,1511,1811,
%T 1889,1901,1931,2459,2699,2819,3449,3491,3539,3821,3911,5081,5399,
%U 5441,5849,6101,6131,6449,7079,7151,7349,7901,8969,9221,10589,10691,10709,11171
%N Numbers n such that n, 2n+1, and 4n+3 all prime.
%C The corresponding primes 2n+1 and 4n+3 respectively have n-1 and 2n primitive roots. - _Lekraj Beedassy_, Jan 07 2005
%C At n > 2, a(n) == {11,29} (mod 30). - _Zak Seidov_, Jan 31 2013
%D T. Moreau, personal communication.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A007700/b007700.txt">Table of n, a(n) for n = 1..10000</a>
%H L. Blum, M. Blum, and M. Shub, <a href="http://dx.doi.org/10.1137/0215025">A simple unpredictable pseudorandom number generator</a>, SIAM J. Comput. 15 (1986), no. 2, 364-383.
%p A007700 := proc(n) local p1,p2; p1 := 2*n+1; p2 := 2*p1+1; if isprime(n) = true and isprime(p1)=true and isprime(p2)=true then RETURN(n); fi; end;
%t Select[Range[10^3*3], PrimeQ[ # ]&&PrimeQ[2*#+1]&&PrimeQ[4*#+3] &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008 *)
%t Select[Prime[Range[1500]],AllTrue[{2#+1,4#+3},PrimeQ]&] (* _Harvey P. Dale_, Apr 12 2022 *)
%o (PARI) is(n)=isprime(n)&&isprime(2*n+1)&&isprime(4*n+3) \\ _Charles R Greathouse IV_, Mar 21 2013
%Y Intersection of A005384 and A023213.
%Y Cf. A005385, A023272, A023302, A023330, A057331, A005602.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, _Simon Plouffe_
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