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A123993
Primes p such that p^2 is an interprime = average of two successive primes.
1
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).
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
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Oct 30 2006
STATUS
approved