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

2,1

Links

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

Prog

(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

Crossrefs

Cf. A066195, A091936, A333877, A333878.

Sequence in context: A156009 A215275 A164620 * A156013 A112634 A303281

Adjacent sequences: A333873 A333874 A333875 * A333877 A333878 A333879

Keyword

nonn

Author

Hugo Pfoertner, Apr 08 2020

Status

approved