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A123993
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Primes p such that p^2 is an interprime = average of two successive primes.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Numbers n such that n^2 is an interprime are listed in A075190(n) = {2, 3, 8, 9, 12, 15, 18, 21, 25, 33, 41, 51, 60, 64, ...}. a(n) are the primes from A075190.
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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] (* From Harvey P. Dale, Jan 05 2011 *)
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CROSSREFS
| Cf. A075190, A024675 - Interprimes.
Sequence in context: A059800 A094714 A042475 * A101821 A121475 A196874
Adjacent sequences: A123990 A123991 A123992 * A123994 A123995 A123996
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 30 2006
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