A333876 a(n) is the largest prime 2^(n-1) <= p < 2^n minimizing the Hamming weight of all primes in this interval.

2, 5, 13, 17, 41, 97, 193, 257, 769, 1153, 2113, 4129, 12289, 18433, 40961, 65537, 163841, 270337, 786433, 1179649, 2101249, 4194433, 8650753, 16777729, 50332673, 69206017, 167772161, 270532609, 537133057, 1107296257, 3221225473, 6442713089, 8858370049

Offset: 2

Author

Hugo Pfoertner, Apr 08 2020

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A066195, A091936, A333877, A333878.

Programs

PARI

for(n=2, 10, my(hmin=n+n,pmax); forprime(p=2^(n-1), 2^n, my(h=hammingweight(p)); if(h<=hmin,pmax=p;hmin=h)); print1(pmax,", "))

Python

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def A333876(n):
    for i in range(n):
        q = 2**n-1
        for d in multiset_permutations('0'*i+'1'*(n-1-i)):
            p = q-int(''.join(d),2)
            if isprime(p):
                return p # Chai Wah Wu, Apr 08 2020