A215429 - OEIS

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A215429

Primes of the form (n^2+2)/6 where n^2+1 is prime.

3, 17, 43, 67, 113, 523, 2017, 2243, 4817, 8363, 9283, 16433, 17713, 19267, 30817, 56843, 81667, 97283, 141067, 149153, 185153, 203873, 271363, 279073, 329473, 398353, 400417, 455953, 472643, 481667, 513923, 519793, 530443, 549643, 670673, 684113, 746243

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The corresponding n are in A215248.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

3 is in the sequence because, for n = 4, 4^2 + 1 = 17 and (4^2 + 2)/6 = 3 are primes.

MATHEMATICA

lst={}; Do[ p=n^2+ 1; q=(p+1)/6; If[PrimeQ[p]&&PrimeQ[q], AppendTo[lst, q]], {n, 0, 2500}]; lst

Select[(#+1)/6&/@Select[Range[3000]^2+1, PrimeQ], PrimeQ] (* Harvey P. Dale, May 07 2017 *)