A057324 First member of a prime triple in a p^2 + p - 1 progression.

2, 3, 11, 13, 53, 131, 233, 241, 281, 569, 659, 691, 761, 881, 1693, 2063, 2411, 2521, 2551, 2663, 2729, 2741, 2861, 3089, 4021, 4159, 4201, 4243, 4423, 4793, 6091, 7103, 7229, 7369, 7753, 7829, 8053, 8641, 8669, 9041, 9059, 9539, 9649, 9769, 10513

Offset: 1

Author

Patrick De Geest, Aug 15 2000

Keywords

• nonn

Comments

There exist no such triples of the form p^2 + p + 1 because each third member is always divisible by 3.

Subsequence of A053184. - Pierre CAMI, Sep 13 2013

Examples

			2 -> 2^2+2-1 = 5 -> 5^2+5-1 = 29 hence the prime triple (2,5,29).
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Cf. A053184, A053185, A057325.

Programs

Mathematica

fmpQ[n_]:=AllTrue[NestList[#^2+#-1&,n,2],PrimeQ]; Select[Prime[Range[ 1300]],fmpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 08 2019 *)

PARI

is(n)=for(k=1,3,if(!isprime(n),return(0));n=n^2+n-1);1 \\ Charles R Greathouse IV, Sep 13 2013