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A007700
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Numbers n such that n, 2n+1, and 4n+3 all prime.
(Formerly M1406)
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46
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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
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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T. Moreau, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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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.
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MAPLE
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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;
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MATHEMATICA
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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 *)
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PROG
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(PARI) is(n)=isprime(n)&&isprime(2*n+1)&&isprime(4*n+3) \\ Charles R Greathouse IV, Mar 21 2013
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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STATUS
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approved
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