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

0,1

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A369117 A268436 A249570 * A077019 A139037 A108511

Adjacent sequences: A051649 A051650 A051651 * A051653 A051654 A051655

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Dec 07 1999

Status

approved