A340707 -id:A340707 - cp's OEIS frontend

A226178 Exponents n such that 2^n - previous_prime(2^n) = next_prime(2^n) - 2^n.

2, 6, 12, 76, 181, 1099, 1820, 9229

Offset: 1

Jean-François Alcover, May 30 2013

The differences next_prime(2^n) - 2^n are respectively: 1, 3, 3, 15, 165, 1035, 663, 2211.

If it exists, a(9) > 10000. - Hugo Pfoertner, Feb 06 2021

			2^6 = 64, next prime = 67, previous prime = 61, 67-64 = 64-61 = 3, hence 6 is in the sequence.

Cf. A000079, A014210, A014234, A117387, A145025.

Cf. A013597, A013603, A340707.

Reap[Do[m = 2^n; p = NextPrime[m, -1]; q = NextPrime[m]; If[p + q == 2*m, Print[n]; Sow[n]], {n, 2, 10^4}]][[2, 1]]

isok(n) = my(p=2^n); p-precprime(p-1) == nextprime(p+1) - p; \\ Michel Marcus, Oct 02 2019

for(n=2,1100,my(p2=2^n,pn=nextprime(p2),pp=p2-pn+p2);if(ispseudoprime(pp),if(precprime(p2)==pp,print1(n,", ")))) \\ Hugo Pfoertner, Feb 06 2021

from itertools import count, islice
from sympy import isprime, nextprime
def A226178_gen(): # generator of terms
    return filter(lambda n:isprime(r:=((k:=1<A226178_list = list(islice(A226178_gen(),5)) # Chai Wah Wu, Aug 08 2022

A340707(a(n)) = 0. - Hugo Pfoertner, Feb 06 2021

Offset 1 from Michel Marcus, Oct 02 2019

a(8) from Hugo Pfoertner, Feb 05 2021

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

Original entry on oeis.org

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

Peter Munn, Aug 07 2022

nonn

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

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

Cf. A014210, A014234, A340707.

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

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

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

cp's OEIS Frontend

A226178 Exponents n such that 2^n - previous_prime(2^n) = next_prime(2^n) - 2^n.

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