OFFSET
1,1
COMMENTS
All terms = {11,17} mod 30. - Zak Seidov, May 08 2011
LINKS
Zak Seidov, Table of n, a(n) for n = 1..1000
H. J. Weber, Regularities of Twin, Triplet and Multiplet Prime Numbers, arXiv:1103.0447 [math.NT], 2011-2012.
EXAMPLE
a(3) = 41 because 0^2 + 0 + 41 = 41; 1^2 + 1 + 41 = 43; 2^2 + 2 + 41 = 47; 3^2 + 3 + 41 = 53; 4^2 + 4 + 41 = 61; 5^2 + 5 + 41 = 71; 6^2 + 6 + 41 = 83, all primes.
MATHEMATICA
lst={}; Do[p1=Prime[n]; If[PrimeQ[p2=p1+2] && PrimeQ[p3=p1+6] && PrimeQ[p4=p1+12] && PrimeQ[p5=p1+20] && PrimeQ[p6=p1+30] && PrimeQ[p7=p1+42], AppendTo[lst, p1]], {n, 10^5}]; lst
okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 6}]]; Select[Range[10000], okQ] (* T. D. Noe, Mar 03 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Sep 08 2008
STATUS
approved