A118377 a(n) is the least prime p such that prime(n)# * p# - 1 is prime.

2, 2, 2, 2, 3, 3, 2, 2, 13, 3, 13, 2, 3, 11, 7, 37, 151, 11, 113, 2, 5, 2, 401, 73, 7, 109, 3, 7, 101, 2, 11, 109, 5, 277, 11, 7, 31, 89, 191, 31, 11, 2713, 11, 13, 73, 461, 17, 17, 5, 41, 257, 17, 127, 1307, 53, 71, 281, 829, 139, 269, 137, 7, 41, 19, 107, 89

Offset

1,1

Links

Table of n, a(n) for n=1..66.

Example

2*2-1 = 3 is prime, 2 = p(1)#, so a(1) = 2.
2*3*2-1 = 11 is prime, 2*3 = p(2)#, so a(2) = 2.
2*3*5*2-1 = 59 is prime, 2*3*5 = p(3)#, so a(3) = 2.
2*3*5*7*2-1 = 419 is prime, 2*3*5*7 = p(4)#, so a(4) = 2.
2*3*5*7*11*2*3-1 = 13859 is prime, 2*3*5*7*11 = p(5)#, so a(5) = 3.

Mathematica

pr[n_] := Product[Prime[i], {i, 1, n}]; a[n_] := Module[{prn = pr[n], k = 1}, While[!PrimeQ[prn*pr[k] - 1], k++]; Prime[k]]; Array[a, 50] (* Amiram Eldar, Sep 11 2021 *)

Prog

(PARI) pr(p) = my(pr=1); forprime(q=2, p, pr *= q); pr;
a(n) = my(p=2, P=pr(prime(n))); while (!ispseudoprime(P*pr(p)-1), p = nextprime(p+1)); p; \\ Michel Marcus, Sep 11 2021

Crossrefs

Cf. A002110.

Sequence in context: A366800 A366799 A322168 * A023516 A156607 A093450

Adjacent sequences: A118374 A118375 A118376 * A118378 A118379 A118380

Keyword

nonn

Author

Pierre CAMI, May 15 2006

Extensions

More terms from Amiram Eldar, Sep 11 2021

Status

approved