A057325 -id:A057325 - cp's OEIS frontend

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

Patrick De Geest, Aug 15 2000

nonn

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

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

Cf. A053184, A053185, A057325.

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 *)

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

A229092 First member of a prime 5-tuple in a p^2+p-1 progression.

Original entry on oeis.org

3, 20963909, 45608209, 46939069, 57856709, 73805093, 83307563, 83983931, 89836889, 90151643, 95786459, 98527859, 98886679, 116260099, 118084559, 118955549, 153404593, 155710213, 190926341, 204854891, 221010899, 238175309, 271884073, 295874083, 299614369

Offset: 1

Pierre CAMI, Sep 13 2013

nonn

Subsequence of A057325.

Pierre CAMI, Table of n, a(n) for n = 1..62

Cf. A057325

pqQ[p_]:=AllTrue[Rest[NestList[#^2+#-1&,p,4]],PrimeQ]; Select[Prime[ Range[ 16232600]],pqQ] (* Harvey P. Dale, Oct 16 2021 *)

is(n)=for(k=1,5,if(!isprime(n),return(0));n=n^2+n-1);1 \\ Charles R Greathouse IV, Sep 13 2013

cp's OEIS Frontend

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

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