A057325 First member of a prime quadruple in a p^2+p-1 progression.

3, 11, 53, 1693, 2663, 4423, 16831, 17609, 36229, 49801, 94961, 121493, 150869, 176303, 183761, 188011, 210901, 213833, 218579, 272903, 300301, 329671, 439511, 444791, 453023, 469613, 518813, 531911, 546071, 559703, 570719, 614279, 705781

Offset: 1

Author

Patrick De Geest, Aug 15 2000

Keywords

• nonn

Comments

I found only one prime 5-tuple so far: (3,11,131,17291,298995971).

Subsequence of A057324. - Pierre CAMI, Sep 13 2013

Examples

			3 -> 3^2+3-1 = 11 -> 11^2+11-1 = 131 -> 131^2+131-1 = 17291 hence the quadruple (3,11,131,17291).
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..6778
• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Cf. A053184, A053185, A057324.

Programs

Mathematica

okQ[n_] := And@@PrimeQ/@NestList[#^2 + # - 1 &, n, 3];
Select[ Prime[ Range[ 60000]], okQ] (* Harvey P. Dale, Jan 05 2011 *)

PARI

is(n)=for(k=1,4,if(!isprime(n),return(0));n=n^2+n-1);1 \\ Charles R Greathouse IV, Sep 13 2013

Extensions

Offset changed by Andrew Howroyd, Aug 14 2024