A051702 Distance from n-th prime to closest prime.

1, 1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 6, 2, 2, 4, 2, 2, 4, 4, 6, 4, 2, 2, 2, 2, 4, 4, 4, 2, 2, 2, 2, 6, 4, 4, 6, 2, 2, 2, 2, 2, 2, 12, 4, 2, 2, 4, 2, 2, 6, 6, 6, 2, 2, 4, 2, 2, 10, 4, 2, 2, 4, 6, 6, 2, 2, 4, 6, 6, 6, 4, 4, 6, 4, 4, 8, 2, 2, 2, 2, 4, 4, 6, 4, 2, 2, 4, 8, 4, 4, 4, 4, 6, 2, 2, 6, 6, 6, 6, 2

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Examples

			Closest primes to 2,3,5,7,11 are 3,2,3,5,13.
		

Links

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

Crossrefs

Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.

A046929(n+1) + 1.

Programs

Mathematica

a[n_] := Min[(p = Prime[n]) - NextPrime[p, -1], NextPrime[p] - p]; Table[a[n], {n, 1, 104}] (* Jean-François Alcover, May 27 2013 *)
Join[{1},Min[Differences[#]]&/@Partition[Prime[Range[110]],3,1]] (* Harvey P. Dale, Sep 23 2016 *)

PARI

a(n,p=prime(n))=min(p-precprime(p-1),nextprime(p+1)-p) \\ Charles R Greathouse IV, Feb 06 2017

Extensions

More terms from James Sellers