|
|
A226178
|
|
Exponents n such that 2^n - previous_prime(2^n) = next_prime(2^n) - 2^n.
|
|
2
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The differences next_prime(2^n) - 2^n are respectively: 1, 3, 3, 15, 165, 1035, 663, 2211.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
2^6 = 64, next prime = 67, previous prime = 61, 67-64 = 64-61 = 3, hence 6 is in the sequence.
|
|
MATHEMATICA
|
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]]
|
|
PROG
|
(PARI) isok(n) = my(p=2^n); p-precprime(p-1) == nextprime(p+1) - p; \\ Michel Marcus, Oct 02 2019
(PARI) 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
(Python)
from itertools import count, islice
from sympy import isprime, nextprime
def A226178_gen(): # generator of terms
return filter(lambda n:isprime(r:=((k:=1<<n)<<1)-(m:=nextprime(k))) and nextprime(r)==m, count(1))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,hard,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|