|
%I #25 Sep 08 2022 08:46:04
%S 37,577,1657,2089,2557,3061,4177,4789,5437,6121,6841,8389,12889,17137,
%T 18289,19477,21961,27361,36541,38197,41617,45181,47017,48889,54721,
%U 56737,58789,74161,78877,83737,88741,91297,93889,96517,99181,113041,121789,124777
%N Primes of the form 2*n^2 + 78*n + 37.
%C Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.
%C 2*a(n) + 1447 is a square. - _Vincenzo Librandi_, Apr 09 2015
%H Vincenzo Librandi, <a href="/A217501/b217501.txt">Table of n, a(n) for n = 1..3000</a>
%t Select[Table[2 n^2 + 78 n + 37, {n, 0, 600}], PrimeQ]
%o (Magma) [a: n in [0..600] | IsPrime(a) where a is 2*n^2+78*n+37];
%Y Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (k=0), A154577 (k=2), A154592 (k=3), A154601 (k=4), A217494 (k=7), A217495 (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A217499 (k=16), A217500 (k=17), this sequence (k=18), A217620 (k=19), A217621 (k=21).
%Y Cf. A054723.
%Y Subsequence of A002144.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Oct 09 2012
|
