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A333876 a(n) is the largest prime 2^(n-1) <= p < 2^n minimizing the Hamming weight of all primes in this interval. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
LINKS
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
Sequence in context: A156009 A215275 A164620 * A156013 A112634 A303281
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Apr 08 2020
STATUS
approved

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Last modified May 21 13:39 EDT 2024. Contains 372736 sequences. (Running on oeis4.)