Voozh

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

(list; graph; refs; listen; history; text; internal format)

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

EXAMPLE

The two closest primes to 23 are 19 and 29. The closest of these (19) is 4 units away. Since 23 is the smallest such number, a(4) = 23. - Michael B. Porter, Oct 24 2025

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