A123993 Primes p such that p^2 is an interprime = average of two successive primes.

2, 3, 41, 907, 1151, 1553, 1609, 1667, 1801, 1907, 1933, 2351, 2473, 2531, 2953, 3001, 3571, 4007, 4073, 4253, 4663, 5023, 5417, 5881, 6143, 6257, 6329, 6343, 7879, 8461, 8521, 8563, 9041, 9067, 10103, 10781, 11243, 11251, 11257, 12097, 12413, 13217

Offset: 1

Author

Alexander Adamchuk, Oct 30 2006

Keywords

• nonn

Comments

Primes in A075190 (numbers n such that n^2 is an interprime).

Crossrefs

Cf. A075190, A024675 (interprimes).

Programs

Mathematica

Select[PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Select[ Range[25000], 2#^2 == PrevPrim[ #^2] + NextPrim[ #^2] &],PrimeQ]
atsp[n_]:=Module[{n2=n^2},(NextPrime[n2]+NextPrime[n2,-1])/2==n2]; Select[Prime[Range[2000]],atsp]  (* Harvey P. Dale, Jan 05 2011 *)

PARI

isok(p) = isprime(p) && ((nextprime(p^2) + precprime(p^2)) / 2 - p^2 == 0); \\ Michel Marcus, Dec 11 2020