A225809 Primes p such that p+q+1 is the square of a prime, where q is the next prime after p.

3, 11, 59, 139, 179, 419, 919, 1399, 3119, 5099, 6379, 8059, 9377, 16007, 31489, 39461, 60899, 83639, 87767, 92867, 100799, 135719, 161879, 163019, 166457, 179393, 206699, 218459, 229157, 273059, 317599, 338659, 363799, 367219, 389839, 411311, 442733, 491039

Offset

1,1

Comments

Terms from Charles R Greathouse IV.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Example

11+13+1=25=5^2 with 5 a prime.

Mathematica

Select[Partition[Prime[Range[41000]], 2, 1], PrimeQ[Sqrt[Total[#]+1]]&][[All, 1]] (* Harvey P. Dale, Apr 17 2022 *)

Prog

(PARI) p=2; forprime(q=3, 1e9, if(issquare(p+q+1, &t)&&isprime(t), print1(p", ")); p=q) \\ Charles R Greathouse IV, Aug 27 2013
(Magma) [p: p in PrimesUpTo(5*10^5) | IsSquare(t) and IsPrime(Isqrt(t)) where t is p+NextPrime(p)+1]; // Bruno Berselli, Aug 28 2013

Crossrefs

Sequence in context: A107007 A199854 A242384 * A267607 A319248 A340865

Adjacent sequences: A225806 A225807 A225808 * A225810 A225811 A225812

Keyword

nonn

Author

J. M. Bergot, Aug 27 2013

Status

approved