A394782 a(n) is the largest prime of the form prime(n)#/d + d where p# denotes the product of all primes <= p and d divides prime(n)#.

3, 7, 31, 211, 2311, 15017, 102107, 1616621, 22309297, 3234846617, 200560490131, 3710369067407, 27659114866121, 1868965904524297, 307444891294245707, 794857523833903571, 961380175077106319537, 23457676271881394196659, 1571664310216053411175823

Offset

1,1

Comments

d is a squarefree number (A005117).

Prime of the form prime(n)#/d+d with d = A295741(n).

Conjecture: sequence is increasing (i.e., a(n+1) > a(n) for any n >= 1).

Similar conjecture: A295741(n) < prime(n).

Links

Table of n, a(n) for n=1..19.

Example

For n=6, 2*3*5*7*11*13/2 + 2 = 30030/2 + 2 = 15017 is prime, while 30031 is not prime, so a(6) = 15017.

Prog

(PARI) a(n) = my(Primo=vecprod(primes(n))); for(D=1, Primo, if(Primo%D==0 && ispseudoprime(Primo/D+D), return(Primo/D+D)));

Crossrefs

Cf. A002110, A005117, A365021, A182987.

Cf. A006862, A014545, A295741.

Sequence in context: A002585 A365021 A103785 * A289127 A289125 A083772

Adjacent sequences: A394779 A394780 A394781 * A394783 A394784 A394785

Keyword

nonn

Author

Alain Rocchelli, Apr 01 2026

Status

approved