A081413 -id:A081413 - cp's OEIS frontend

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

Labos Elemer, Apr 02 2003

nonn

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

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

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

Cf. A001223, A006530, A081413, A000230.

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

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 *)

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

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

A081414 Largest prime divisor of prime(2^n+1) - prime(2^n).

Original entry on oeis.org

1, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 3, 5, 2, 3, 3, 2, 3, 2, 13, 5, 17, 2, 5, 5, 5, 2, 5, 3, 7, 2, 3, 11, 3, 3, 13, 5, 11, 2, 5, 3, 3, 5, 7, 2, 3, 3, 2, 7, 2, 5, 7, 3, 7, 37, 7, 5, 17, 7, 11, 11, 13, 3, 3, 3, 43, 43, 3, 3, 7, 3, 5, 3, 5, 11, 3, 5, 3

Offset: 0

Labos Elemer, Apr 02 2003

nonn

Cf. A006530, A001223, A000079, A081412, A081413, A074325.

a(n) = A006530(A001223(A000079(n))) = A081412(2^n) = A006530(A074325(n)).

Three more terms from Max Alekseyev, May 15 2009

Offset changed to 0, a(0) prepended and more terms added by Amiram Eldar, Jun 04 2024

cp's OEIS Frontend

A081412 Largest prime divisors of differences between consecutive primes.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula