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A007700 n, 2n+1, 4n+3 all prime.
(Formerly M1406)
46
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

The first member of a prime triple (p, q, r) in a 2p+1 progression (q = 2p + 1, r = 2q + 1). Sequence of numbers p*q*r is in A231967. - Jaroslav Krizek, Nov 19 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 *)

s = {2, 5}; a = 11; b = 29; Join[{2, 5}, Reap[Do[If[PrimeQ[a] && PrimeQ[2 a + 1] && PrimeQ[4 a + 3], Sow[a]]; If[PrimeQ[b] && PrimeQ[2 b + 1] && PrimeQ[4 b + 3], Sow[b]]; a = a + 30; b = b + 30, {300}]][[2, 1]]] (* Zak Seidov, Jan 31 2013 *)

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

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Last modified March 24 23:59 EDT 2017. Contains 284035 sequences.