A364920 a(n) is the least prime p > prime(n) such that p * prime(n)# + 1 is prime, where q# denotes the product of all primes <= q.

3, 5, 7, 11, 19, 29, 29, 31, 31, 31, 61, 59, 71, 53, 61, 149, 109, 101, 197, 113, 113, 139, 179, 131, 233, 127, 137, 113, 191, 223, 191, 151, 241, 311, 167, 199, 167, 191, 401, 227, 277, 197, 257, 263, 233, 277, 389, 251, 263, 373, 499, 503, 311, 487, 433, 283

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Formula

Limit_{N->oo} (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n)) = 3/2.

Mathematica

a[n_] := Module[{p = Prime[n + 1], pr = Product[Prime[i], {i, 1, n}]}, While[! PrimeQ[p*pr + 1], p = NextPrime[p]]; p]; Array[a, 100] (* Amiram Eldar, Aug 12 2023 *)

Prog

(PARI) a(n) = my(p=nextprime(prime(n)+1), P=vecprod(primes(n))); while (!ispseudoprime(p*P+1), p=nextprime(p+1)); p; \\ Michel Marcus, Aug 13 2023

Crossrefs

Cf. A002110.

Sequence in context: A161420 A071997 A093442 * A155008 A367195 A175196

Adjacent sequences: A364917 A364918 A364919 * A364921 A364922 A364923

Keyword

nonn

Author

Alain Rocchelli, Aug 12 2023

Status

approved