A247197 Primes p such that 2*p^2 + 3 and 2*p^2 + 5 are also primes.
2, 7, 23, 47, 887, 1297, 1657, 2207, 2357, 2753, 4583, 4657, 6967, 8353, 8363, 10453, 12203, 12343, 13967, 16217, 16903, 21737, 23357, 23497, 25447, 29017, 32363, 36083, 40847, 41603, 41617, 43633, 45757, 46933, 48407, 52313, 60167, 60457, 66173, 67867, 71713, 72497, 72823, 73897
Offset: 1
Keywords
Examples
2 is in this sequence because 2*2^2 + 3 = 11, 2*2^2 + 5 = 13 and 2 are all primes.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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Magma
[ n: n in [1..70000] | IsPrime(n) and IsPrime(2*(n^2+2)-1) and IsPrime(2*(n^2+2)+1) ];
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Mathematica
a247197[n_Integer] := Select[Prime /@ Range[n], And[PrimeQ[2*#^2 + 3], PrimeQ[2*#^2 + 5]] &]; a247197[7500] (* Michael De Vlieger, Nov 30 2014 *) Select[Prime[Range[7300]],AllTrue[2#^2+{3,5},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 21 2019 *)
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