A065316 Largest prime divisor of n-th primorial - (n+1)-st prime.

23, 199, 2297, 30013, 12451, 9699667, 79139, 122069683, 9241993, 77184383, 211941187, 72280449346243, 73629553, 142226610221, 131076443530861861, 382046844818915214929, 1348764323657, 1822793973448088839487, 217379667530071, 3217644767340672907899084554047, 267064515689275851355624017992701

Offset: 3

Author

Labos Elemer, Oct 29 2001

Keywords

• nonn

Examples

			For n=3, 3rd primorial=30, 4th prime=7, difference=23, so a(3)=23.
		

Links

• Tyler Busby, Table of n, a(n) for n = 3..89 (terms 3..80 from Sean A. Irvine)
• Romeo Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2023. - From _N. J. A. Sloane_, Jun 13 2012

Crossrefs

Cf. A002110, A000040, A006530, A006530, A057713, A002584, A002585, A051342.

See also A065314, A065315, A065317.

Programs

Mathematica

Module[{nn=30,pmrl},pmrl=FoldList[Times,Prime[Range[nn]]];FactorInteger[ #][[-1,1]]&/@(Drop[#[[1]]-#[[2]]&/@Thread[ {pmrl,Prime[ Range[ 2,nn+1]]}],2])] (* Harvey P. Dale, Dec 30 2021 *)

PARI

a(n) = vecmax(factor(prod(i=1, n, prime(i)) - prime(n+1))[,1]); \\ Michel Marcus, Aug 29 2019

Formula

a(n) = A006530(A002110(n)-A000040(n+1)).

Extensions

More terms from Michel Marcus, Aug 29 2019