A007700 Numbers n such that n, 2n+1, and 4n+3 all prime. (Formerly M1406)

2, 5, 11, 41, 89, 179, 359, 509, 719, 1019, 1031, 1229, 1409, 1451, 1481, 1511, 1811, 1889, 1901, 1931, 2459, 2699, 2819, 3449, 3491, 3539, 3821, 3911, 5081, 5399, 5441, 5849, 6101, 6131, 6449, 7079, 7151, 7349, 7901, 8969, 9221, 10589, 10691, 10709, 11171

Offset

1,1

Comments

The corresponding primes 2n+1 and 4n+3 respectively have n-1 and 2n primitive roots. - Lekraj Beedassy, Jan 07 2005

At n > 2, a(n) == {11,29} (mod 30). - Zak Seidov, Jan 31 2013

References

T. Moreau, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

L. Blum, M. Blum, and M. Shub, A simple unpredictable pseudorandom number generator, SIAM J. Comput. 15 (1986), no. 2, 364-383.

Maple

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;

Mathematica

Select[Range[10^3*3], PrimeQ[ # ]&&PrimeQ[2*#+1]&&PrimeQ[4*#+3] &] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
Select[Prime[Range[1500]], AllTrue[{2#+1, 4#+3}, PrimeQ]&] (* Harvey P. Dale, Apr 12 2022 *)

Prog

(PARI) is(n)=isprime(n)&&isprime(2*n+1)&&isprime(4*n+3) \\ Charles R Greathouse IV, Mar 21 2013

Crossrefs

Intersection of A005384 and A023213.

Cf. A005385, A023272, A023302, A023330, A057331, A005602.

Sequence in context: A191029 A106886 A237814 * A071313 A172297 A128231

Adjacent sequences: A007697 A007698 A007699 * A007701 A007702 A007703

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Status

approved