A187060 - OEIS

%I #29 Aug 10 2017 03:30:59

%S 11,17,41,21557,26681,128981,844427,2073347,3992201,4889237,6184637,

%T 11900501,21456047,24598361,33771581,34864211,50943791,51448361,

%U 51867197,55793951,56421347,61218251,67787537,69726647,76345121

%N Primes p such that the polynomial x^2 + x + p generates only primes for x = 1..7.

%C From Weber, p. 15. However, erroneous.

%C All terms = {11,17} mod 30. - _Zak Seidov_, May 08 2011

%H Zak Seidov and Charles R Greathouse IV, <a href="/A187060/b187060.txt">Table of n, a(n) for n = 1..10000</a> (Zak Seidov found the first 400 terms)

%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(4) <> 21577 because 0^2 + 0 + 21577 = 21577; 1^2 + 1 + 21577 = 21579 = 3 * 7193 thus exposing an error in Weber's paper; 2^2 + 2 + 21577 = 21583 = 113 * 191; 3^2 + 3 + 21577 = 21589 is prime; 4^2 + 4 + 21577 = 21597 = 3 * 23 * 313; 5^2 + 5 + 21577 = 21607 = 17 * 31 * 41 (a "3-brilliant number" rather than a prime); 6^2 + 6 + 21577 = 21619 = 13 * 1663; 7^2 + 7 + 21577 = 21633 = 3 * 7211.

%t okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 7}]]; Select[Range[10000], okQ] (* _T. D. Noe_, Mar 03 2011 *)

%o (PARI) for(k=1,50000,p=prime(k); if(isprime(p+2) && isprime(p+6) && isprime(p+12) && isprime(p+20) && isprime(p+30) && isprime(p+42) && isprime(p+56),print(p),)) \\ _Nathaniel Johnston_, Apr 26 2011

%o (PARI) p=2;q=3;forprime(r=5,1e6,if(r-p==6 && q-p==2 && isprime(p+12) && isprime(p+20) && isprime(p+30) && isprime(p+42) && isprime(p+56),print(p));p=q;q=r) \\ _Charles R Greathouse IV_, Mar 04 2012

%Y Cf. A187057, A187058, A144051.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Mar 03 2011

%E a(12)-a(25) from _Nathaniel Johnston_, Apr 26 2011