OFFSET
1,1
COMMENTS
From Weber, p. 15. However, erroneous.
All terms = {11,17} mod 30. - Zak Seidov, May 08 2011
LINKS
Zak Seidov and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (Zak Seidov found the first 400 terms)
H. J. Weber, Regularities of Twin, Triplet and Multiplet Prime Numbers, arXiv:1103.0447 [math.NT], 2011-2012.
EXAMPLE
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.
MATHEMATICA
okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 7}]]; Select[Range[10000], okQ] (* T. D. Noe, Mar 03 2011 *)
PROG
(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
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Mar 03 2011
EXTENSIONS
a(12)-a(25) from Nathaniel Johnston, Apr 26 2011
STATUS
approved