A283563 - OEIS

%I #17 Mar 12 2017 06:48:13

%S 1,2,3,4,5,6,11,18,22,71

%N Numbers n such that A112368(n) = Sum_{i=0..n} 2^i*i! is prime.

%C All the terms of A112368 starting from a(72) are divisible by 73.

%C The first 9 associated primes are 3, 11, 59, 443, 4283, 50363, 85662309563, 1726380042510080613563, 4824162806180387282426469563. The 10th and last term is about 2.022... * 10^123.

%H Amiram Eldar, <a href="/A283563/b283563.txt">Table of n, a(n) for n = 1..10</a>

%e 1 is in this sequence because 2^0*0! + 2^1*1! = 3 is prime.

%t A112368[n_] := Sum[2^i*i!, {i, 0, n}]; Select[Range[0, 1000], PrimeQ[A112368[#]] &]

%o (PARI) isok(n) = isprime(sum(i=0, n, 2^i*i!)); \\ _Michel Marcus_, Mar 11 2017

%Y Cf. A112368.

%K nonn,fini,full

%O 1,2

%A _Amiram Eldar_, Mar 11 2017