A333877 a(n) is the largest prime 2^(n-1) <= p < 2^n maximizing the Hamming weight of all primes in this interval.
3, 7, 13, 31, 61, 127, 251, 509, 1021, 2039, 4093, 8191, 16381, 32749, 65519, 131071, 262139, 524287, 1048573, 2097143, 4194301, 8388587, 16777213, 33546239, 67108859, 134217467, 260046847, 536870909, 1073741567, 2147483647, 4294967291, 8589934583, 16911433727
Offset: 2
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 2..998
Programs
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Maple
a:= proc(n) option remember; local i, p; for i from 0 do p:= max(select(isprime, map(l-> add(l[j]* 2^(j-1), j=1..n), combinat[permute]([1$(n-i),0$i])))); if p>0 then break fi od; p end: seq(a(n), n=2..30); # Alois P. Heinz, Apr 23 2020 -
Mathematica
a[n_] := a[n] = MaximalBy[{#, DigitCount[#, 2, 1]}& /@ Select[Range[ 2^(n-1), 2^n-1], PrimeQ], Last][[-1, 1]]; Table[Print[n, " ", a[n]]; a[n], {n, 2, 30}] (* Jean-François Alcover, Nov 09 2020 *) -
PARI
for(n=2, 30, my(hmax=0,pmax); forprime(p=2^(n-1), 2^n, my(h=hammingweight(p)); if(h>=hmax,pmax=p;hmax=h)); print1(pmax,", "))
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Python
from sympy import isprime from sympy.utilities.iterables import multiset_permutations def A333877(n): for i in range(n-1,-1,-1): 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
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