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

3,1

Links

Sean A. Irvine, Table of n, a(n) for n = 3..80

R. 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], 2012-2018. - From N. J. A. Sloane, Jun 13 2012

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A002110, A000040, A006530, A006530, A057713, A002584, A002585, A051342 A065314-A065317.

Sequence in context: A307355 A058193 A065314 * A060882 A367182 A221670

Adjacent sequences: A065313 A065314 A065315 * A065317 A065318 A065319

Keyword

nonn

Author

Labos Elemer, Oct 29 2001

Extensions

More terms from Michel Marcus, Aug 29 2019

Status

approved