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A247175
Numbers n such that 2*(n^2 + 2) - 1 and 2*(n^2 + 2) + 1 are both prime.
2
0, 1, 2, 7, 23, 47, 98, 208, 268, 278, 352, 422, 712, 803, 833, 887, 1022, 1048, 1052, 1057, 1297, 1372, 1517, 1603, 1657, 1717, 1748, 1888, 1988, 2102, 2207, 2233, 2357, 2548, 2567, 2753, 2828, 2893, 2938, 3017, 3362, 3367, 3572, 3817, 3908, 4247, 4268, 4312, 4403, 4408, 4412, 4478
OFFSET
1,3
COMMENTS
Numbers n such that 2*n^2 + 3 and 2*n^2 + 5 are both prime.
LINKS
EXAMPLE
2 is in this sequence because 2*2^2 + 3 = 11 and 2*2^2 + 5 = 13 are both prime.
MATHEMATICA
a247175[n_Integer] := Select[Range[n], And[PrimeQ[2*(#^2 + 2) - 1], PrimeQ[2*(#^2 + 2) + 1]] &]; a247175[4500] (* Michael De Vlieger, Nov 30 2014 *)
Select[Range[0, 4500], AllTrue[2#^2+{3, 5}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 09 2019 *)
PROG
(Magma) [ n: n in [0..4500] | IsPrime(2*(n^2+2)-1) and IsPrime(2*(n^2+2)+1) ];
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved