A131580 Least prime P such that P^(2*prime(n))-P^prime(n)-1 is prime with prime(n) the n-th prime.

2, 3, 2, 3, 163, 19, 151, 263, 131, 3041, 311, 401, 2029, 1163, 2309, 157, 541, 61, 739, 563, 1097, 4813, 1801, 1399, 709, 317, 14563, 863, 5479, 337, 2351, 9533, 4931, 401, 1117, 14639, 17791, 1409, 571, 5171, 16633, 7001, 2129, 10891, 31151, 22709, 6079, 883, 20113

Offset

1,1

Links

Daniel Suteu, Table of n, a(n) for n = 1..100

Example

2^(2*2)-2^2-1=11 prime, 2 is prime, so P = a(1) = 2.
2^(2*3)-2^3-1=55 composite; 3^(2*3)-3^3-1=701 prime, 3 is prime so P = a(2) = 3.

Mathematica

s={}; Do[pp=2; np=Prime[n]; While[!PrimeQ[pp^(2np)-pp^np-1], pp=NextPrime[pp]]; AppendTo[s, pp], {n, 40}]; s (* James C. McMahon, Feb 25 2025 *)

Prog

(PARI) a(n) = my(p = prime(n), P=2); while(!isprime(P^(2*p)-P^p-1), P = nextprime(P+1)); P; \\ Michel Marcus, Sep 15 2019
(Magma) sol:=[]; for n in [1..31] do p:=2;  while not IsPrime(p^(2*q)-p^ NthPrime(n)-1) where q is NthPrime(n) do p:=NextPrime(p); end while; Append(~sol, p); end for; sol; // Marius A. Burtea, Sep 15 2019

Crossrefs

Sequence in context: A177799 A125767 A326991 * A087038 A299115 A179590

Adjacent sequences: A131577 A131578 A131579 * A131581 A131582 A131583

Keyword

nonn,changed

Author

Pierre CAMI, Aug 29 2007

Extensions

a(33)-a(49) from Daniel Suteu, Sep 15 2019

Status

approved