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Primes of the form 2*n^2+66*n+31.
2

%I #9 Sep 08 2022 08:46:08

%S 499,787,1471,1867,2767,3271,4999,5647,8599,13099,14107,16231,19687,

%T 22171,24799,33547,40099,43591,52951,63211,65371,67567,79087,88951,

%U 94099,99391,104827,107599,116131,119047,124987,131071,153499,160231,167107,177691,192307

%N Primes of the form 2*n^2+66*n+31.

%C Primes of the form 36*A056115(k)+31.

%C Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.

%H Vincenzo Librandi, <a href="/A243957/b243957.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Table[2 n^2 + 66 n + 31, {n, 800}], PrimeQ]

%o (Magma) [a: n in [1..500] | IsPrime(a) where a is 2*n^2+66*n+31];

%Y Cf. A056115, A142110 (supersequence).

%Y Cf. similar sequences listed in A243888.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Jun 16 2014