A065314 Smallest prime divisor of (n-th primorial - (n+1)-st prime).

23, 199, 2297, 30013, 41, 9699667, 2819, 53, 21701, 79, 163, 181, 61, 1619, 14669, 307, 103, 306091, 907, 3217644767340672907899084554047, 267064515689275851355624017992701, 23768741896345550770650537601358213

Offset

3,1

Links

Sean A. Irvine, Table of n, a(n) for n = 3..80 (terms 3..40 from Michel Marcus)

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. - N. J. A. Sloane, Jun 13 2012

Formula

a(n) = A020639( A002110(n) - A000040(n+1) ).

Example

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

Mathematica

Map[FactorInteger[Times @@ #1 - #2][[1, 1, 1]] & @@ Reverse@ TakeDrop[#, -1] &, Drop[#, 3] &@ FoldList[Flatten@ Append[{#1}, #2] &, Prime@ Range@ 25]] (* Michael De Vlieger, Jul 16 2017 *)

Prog

(PARI) a(n) = vecmin(factor(prod(k=1, n, prime(k)) - prime(n+1))[, 1]); \\ Michel Marcus, Jul 16 2017

Crossrefs

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

Sequence in context: A108646 A307355 A058193 * A065316 A060882 A367182

Adjacent sequences: A065311 A065312 A065313 * A065315 A065316 A065317

Keyword

nonn

Author

Labos Elemer, Oct 29 2001

Status

approved