A051700 Distance from n to closest prime that is different from n.

2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 1, 6, 1, 2, 3, 4, 3, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1

Offset

0,1

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Example

Closest primes to 0,1,2,3,4 are 2,2,3,2,3.

Maple

with(numtheory); f := n->min(nextprime(n)-n, n-prevprime(n));

Mathematica

Table[Min[NextPrime[n]-n, n-NextPrime[n, -1]], {n, 0, 200}]  (* Harvey P. Dale, Mar 27 2011 *)

Prog

(Python)
from sympy import prevprime, nextprime
def A051700(n): return [2, 1, 1][n] if n < 3 else min(n-prevprime(n), nextprime(n)-n)
print([A051700(n) for n in range(105)]) # Michael S. Branicky, Oct 26 2025

Crossrefs

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

Sequence in context: A354747 A254444 A102005 * A337006 A025892 A025883

Adjacent sequences: A051697 A051698 A051699 * A051701 A051702 A051703

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from James Sellers

Status

approved