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

1,1

Comments

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

Links

Table of n, a(n) for n=1..42.

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 *)

Prog

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

Crossrefs

Cf. A075190, A024675 (interprimes).

Sequence in context: A200817 A042475 A241277 * A351820 A271331 A101821

Adjacent sequences: A123990 A123991 A123992 * A123994 A123995 A123996

Keyword

nonn

Author

Alexander Adamchuk, Oct 30 2006

Status

approved