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

0,1

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Sequence in context: A038075 A032236 A128776 * A113842 A032161 A265801

Adjacent sequences: A117384 A117385 A117386 * A117388 A117389 A117390

Keyword

nonn

Author

Lekraj Beedassy, Mar 11 2006

Extensions

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

Status

approved