A187058 - OEIS

%I #25 Aug 05 2017 03:09:58

%S 11,17,41,1277,1607,3527,13901,21557,26681,28277,31247,33617,55661,

%T 68897,97367,113147,128981,166841,195731,221717,347981,348431,354371,

%U 416387,421697,506327,548831,566537,665111,844427,929057,954257

%N Primes p such that the polynomial x^2 + x + p generates only primes for x = 1..5.

%C From Weber, p. 15.

%C This sequence is infinite, assuming Dickson's conjecture.

%C All terms = {11, 17} mod 30. - _Zak Seidov_, May 07 2011

%H Charles R Greathouse IV, <a href="/A187058/b187058.txt">Table of n, a(n) for n = 1..10000</a>, replacing a b-file from Zak Seidov.

%H H. J. Weber, <a href="http://arxiv.org/abs/1103.0447">Regularities of Twin, Triplet and Multiplet Prime Numbers</a>, arXiv:1103.0447 [math.NT], 2011-2012.

%e a(2) = 17 because x^2 + x + 17 generates 0^2 + 0 + 17 = 17; 1^2 + 1 + 17 = 19; 2^2 + 2 + 17 = 23; 3^2 + 3 + 17 = 29; 4^2 + 4 + 17 = 37; and 5^2 + 5 + 17 = 47, all primes.

%t okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 5}]]; Select[Range[10000], okQ] (* _T. D. Noe_, Mar 03 2011 *)

%o (PARI) forprime(p=9,1e6,if((p%30==11 || p%30==17) && isprime(p+2) && isprime(p+6) && isprime(p+12) && isprime(p+20) && isprime(p+30), print1(p", "))) \\ _Charles R Greathouse IV_, May 08 2011

%Y Cf. A144051, A187057, A187060.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Mar 03 2011