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 A007700 Numbers n such that n, 2n+1, and 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 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

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Last modified September 28 03:41 EDT 2023. Contains 365715 sequences. (Running on oeis4.)