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

0,1

Links

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

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).

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 *)

Prog

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

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.

Sequence in context: A034438 A079280 A038750 * A300439 A208818 A221835

Adjacent sequences: A356431 A356432 A356433 * A356435 A356436 A356437

Keyword

nonn

Author

Peter Munn, Aug 07 2022

Status

approved