A081412 Largest prime divisors of differences between consecutive primes.

2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 7, 2, 3, 2, 5, 2, 3, 3, 2, 3, 3, 2, 5, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 5, 3, 3, 3, 2, 3, 2, 2, 5, 7, 2, 2, 2, 7, 3, 5, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 5, 2, 5, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 3, 5, 3, 3, 2, 3, 5

Offset: 2

Author

Labos Elemer, Apr 02 2003

Keywords

• nonn

Comments

If a(n)=2, then corresponding prime-difference is a power of 2.

a(n)=2 for twin-prime differences.

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A001223, A006530, A081413, A000230.

Programs

Maple

lpf:= t -> max(numtheory:-factorset(t)):
P:= [seq(ithprime(i),i=1..200)]:
G:= P[2..-1]-P[1..-2]:
A:= map(lpf,G[2..-1]): # Robert Israel, Mar 03 2025

Mathematica

Table[FactorInteger[Prime[w+1]-Prime[w]][[ -1, 1]], {w, 2, 256}]
FactorInteger[#][[-1,1]]&/@Differences[Prime[Range[2,110]]] (* Harvey P. Dale, Sep 24 2017 *)

PARI

a(n) = vecmax(factor(prime(n+1)-prime(n))[, 1]); \\ Michel Marcus, Mar 27 2020

Formula

a(n) = A006530(A001223(n)).