A285528 Numbers n such that A217723(n) (sum of first n primorial numbers minus 1) is prime.

2, 3, 5, 6, 7, 8, 11, 14, 21, 41, 42, 43, 74, 78

Offset: 1

Author

Amiram Eldar, Apr 20 2017

Keywords

• nonn
• fini
• full

Comments

This sequence is finite since 463 (the 90th prime) divides A217723(89) and thus all the succeeding terms of A217723 are also divisible by 463.

The associated primes are: 7, 37, 2557, 32587, 543097, 10242787, 207263519017, 13394639596851067, 41295598995285955839203627497, 2.998... * 10^70, 5.427... * 10^72, 1.036... * 10^75, 4.549... * 10^150 and 1.019... * 10^161. They are a subsequence of A127729.

Examples

			A217723(5) = 2 + 2*3 + 2*3*5 + 2*3*5*7 + 2*3*5*7*11 - 1 = 2557 is prime, thus 5 is in this sequence.
		

Crossrefs

Cf. A002110, A217723, A127729, A223546.

Programs

Maple

select(m -> isprime(add(mul(ithprime(i),i=1..j),j=1..m)-1), [$1..89]); # Robert Israel, Apr 20 2017

Mathematica

primorial[n_] := Product[Prime[i], {i, n}]; a[n_] := Sum[primorial[i], {i, 1, n}]-1; Select[Range[0, 100], PrimeQ[a[#]] &]
(* Second program: *)
Flatten@ Position[Accumulate@ FoldList[#1 #2 &, Prime@ Range@ 200] - 1 /. k_ /; k == 1 || CompositeQ@ k -> 0, m_ /; m != 0] (* Michael De Vlieger, Apr 23 2017 *)