A356434 Prime nearest to 2^n. In case of a tie, choose the larger.

2, 2, 5, 7, 17, 31, 67, 127, 257, 509, 1021, 2053, 4099, 8191, 16381, 32771, 65537, 131071, 262147, 524287, 1048573, 2097143, 4194301, 8388617, 16777213, 33554467, 67108859, 134217757, 268435459, 536870909, 1073741827, 2147483647, 4294967291, 8589934583

Offset: 0

Author

Peter Munn, Aug 07 2022

Keywords

• nonn

Links

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

Crossrefs

A117387 differs by preferring the smaller prime in the case of a tie, which occurs when n is in A226178.

Cf. A014210, A014234, A340707.

Programs

Mathematica

Join[{2,2},Table[Max[Nearest[{NextPrime[2^n,-1],NextPrime[2^n]},2^n]],{n,2,40}]] (* Harvey P. Dale, Feb 19 2023 *)

Python

from sympy import prevprime, nextprime
def A356434(n): return (r if (m:=nextprime(k:=1< (k<<1)-(r:=prevprime(k)) else m) if n>1 else 2 # Chai Wah Wu, Aug 08 2022

Formula

a(0) = 2; for n >= 1, if A014210(n) + A014234(n) > 2^(n+1) then a(n) = A014234(n), otherwise a(n) = A014210(n).