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

1,1

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.

Links

Table of n, a(n) for n=1..14.

Example

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.

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 *)

Crossrefs

Cf. A002110, A217723, A127729, A223546.

Sequence in context: A016741 A191167 A006431 * A151894 A352328 A028229

Adjacent sequences: A285525 A285526 A285527 * A285529 A285530 A285531

Keyword

nonn,fini,full

Author

Amiram Eldar, Apr 20 2017

Status

approved