A247175 Numbers n such that 2*(n^2 + 2) - 1 and 2*(n^2 + 2) + 1 are both prime.
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
Keywords
Examples
2 is in this sequence because 2*2^2 + 3 = 11 and 2*2^2 + 5 = 13 are both prime.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Magma
[ n: n in [0..4500] | IsPrime(2*(n^2+2)-1) and IsPrime(2*(n^2+2)+1) ];
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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 *)
Comments