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

2,1

Comments

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

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

Links

Table of n, a(n) for n=2..106.

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A001223, A006530, A081413, A000230.

Sequence in context: A052298 A366441 A179938 * A082863 A278950 A029411

Adjacent sequences: A081409 A081410 A081411 * A081413 A081414 A081415

Keyword

nonn

Author

Labos Elemer, Apr 02 2003

Status

approved