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A031131

Difference between n-th prime and (n+2)-nd prime.

3, 4, 6, 6, 6, 6, 6, 10, 8, 8, 10, 6, 6, 10, 12, 8, 8, 10, 6, 8, 10, 10, 14, 12, 6, 6, 6, 6, 18, 18, 10, 8, 12, 12, 8, 12, 10, 10, 12, 8, 12, 12, 6, 6, 14, 24, 16, 6, 6, 10, 8, 12, 16, 12, 12, 8, 8, 10, 6, 12, 24, 18, 6, 6, 18, 20, 16, 12, 6, 10, 14, 14, 12, 10, 10, 14, 12, 12, 18, 12, 12, 12

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OFFSET

1,1

COMMENTS

Distance between the pair of primes adjacent to the (n+1)-st prime. - Lekraj Beedassy, Oct 01 2004 [Typo corrected by Zak Seidov, Feb 22 2009]

A031131(A261525(n)) = 2*n and A031131(m) != 2*n for m < A261525(n). - Reinhard Zumkeller, Aug 23 2015

The Polymath project 8b proved that a(n) <= 395106 infinitely often (their published paper contains the slightly weaker bound a(n) <= 398130 infinitely often). - Charles R Greathouse IV, Jul 22 2016

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

D. H. J. Polymath, Variants of the Selberg sieve, and bounded intervals containing many primes, Research in the Mathematical Sciences 1:12 (2014).

Polymath project, Bounded gaps between primes

FORMULA

a(n) = A001223(n) + A001223(n-1). - Lior Manor, Jan 19 2005

a(n) = A000040(n+2) - A000040(n).

a(n) = 2*A052288(n-1) for n>1. - Hugo Pfoertner, Apr 16 2025

EXAMPLE

a(10)=8 because the 10th prime=29 is followed by primes 31 and 37, and 37 - 29 = 8.

MAPLE

P:= select(isprime, [2, seq(2*i+1, i=1..1000)]):