A051652 Smallest number at distance n from nearest prime.

2, 1, 0, 26, 23, 118, 53, 120, 409, 532, 293, 1140, 211, 1340, 1341, 1342, 1343, 1344, 2179, 15702, 3967, 15704, 15705, 19632, 16033, 19634, 19635, 31424, 31425, 31426, 24281, 31428, 31429, 31430, 31431, 31432, 31433, 155958, 155959, 155960, 38501

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..228 (terms 0..91 from _R. J. Mathar_)
• Michael S. Branicky, Python program

Crossrefs

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

Programs

Maple

A051700 := proc(m) option remember ; if m <= 2 then op(m+1,[2,1,1]) ; else min(nextprime(m)-m,m-prevprime(m)) ; fi ; end:
A051652 := proc(n) local m ; if n = 0 then RETURN(2); else for m from 0 do if A051700(m) = n then RETURN(m) ; fi ; od: fi ; end:
for n from 0 to 79 do printf("%d %d\n",n,A051652(n)); od: # R. J. Mathar, Jul 22 2009

Mathematica

A051700[n_] := A051700[n] = Min[ NextPrime[n] - n, n - NextPrime[n, -1]]; a[n_] := For[m = 0, True, m++, If[A051700[m] == n, Return[m]]]; a[0] = 2; Table[ a[n], {n, 0, 40}] (* Jean-François Alcover, Dec 19 2011, after R. J. Mathar *)
Join[{2,1,0},Drop[Flatten[Table[Position[Table[Min[NextPrime[n]-n, n-NextPrime[ n,-1]],{n,200000}],?(#==i&),{1},1],{i,40}]],2]] (* _Harvey P. Dale, Mar 16 2015 *)

Python

# see link for faster program
from sympy import prevprime, nextprime
def A051700(n):
  return [2, 1, 1][n] if n < 3 else min(n-prevprime(n), nextprime(n)-n)
def a(n):
  if n == 0: return 2
  m = 0
  while A051700(m) != n: m += 1
  return m
print([a(n) for n in range(26)]) # Michael S. Branicky, Feb 27 2021

Extensions

More terms from James Sellers, Dec 07 1999