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

1,3

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

A046929(n+1) + 1.

Sequence in context: A003642 A100007 A104369 * A073130 A238267 A143526

Adjacent sequences: A051699 A051700 A051701 * A051703 A051704 A051705

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers

Status

approved