A117387 Prime nearest to 2^n. In case of a tie, choose the smaller.

2, 2, 3, 7, 17, 31, 61, 127, 257, 509, 1021, 2053, 4093, 8191, 16381, 32771, 65537, 131071, 262147, 524287, 1048573, 2097143, 4194301, 8388617, 16777213, 33554467, 67108859, 134217757, 268435459, 536870909, 1073741827, 2147483647, 4294967291, 8589934583

Offset: 0

Author

Lekraj Beedassy, Mar 11 2006

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Programs

Mathematica

f[n_] := Block[{k = 0}, While[ !PrimeQ[2^n - k] && !PrimeQ[2^n + k], k++ ]; Min@Select[{2^n - k, 2^n + k}, PrimeQ@# &]]
pn2n[n_]:=Module[{c=2^n,a,b},a=NextPrime[c,-1];b=NextPrime[c];If[b-c < c-a,b,a]]; Join[{2,2},Table[pn2n[n],{n,2,40}]] (* Harvey P. Dale, Jul 24 2019 *)

Python

from sympy import prevprime, nextprime
def A117387(n): return (m if (m:=nextprime(k:=1<1 else 2 # Chai Wah Wu, Aug 08 2022

Formula

a(n) = A000079(n) - A059959(n). [Corrected by Georg Fischer, Dec 13 2022]

Extensions

Edited, corrected and extended by Robert G. Wilson v, Mar 14 2006