OFFSET
1,1
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..1000
MATHEMATICA
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 2; Do[c = 0; While[p < 2^n, b = Count[ IntegerDigits[p, 2], 1]; If[c < b, c = b; q = p]; p = NextPrim[p]]; Print[q], {n, 1, 30}] (* Robert G. Wilson v, Feb 21 2004 *)
b[n_] := Min[ Select[ FromDigits[ #, 2] & /@ (Join[{1}, #, {1}] & /@ Permutations[ Join[{0}, Table[1, {n - 2}]]]), PrimeQ[ # ] &]]; c[n_] := Min[ Select[ FromDigits[ #, 2] & /@ (Join[{1}, #, {1}] & /@ Permutations[ Join[{0, 0}, Table[1, {n - 3}]]]), PrimeQ[ # ] &]]; f[n_] := If[ PrimeQ[2^(n + 1) - 1], 2^(n + 1) - 1, If[ PrimeQ[ b[n]], b[n], c[n]]]; Table[ f[n], {n, 30}] (* Robert G. Wilson v *)
PROG
(Python)
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def A091938(n):
for i in range(n, -1, -1):
q = 2**n
for d in multiset_permutations('0'*(n-i)+'1'*i):
p = q+int(''.join(d), 2)
if isprime(p):
return p # Chai Wah Wu, Apr 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 14 2004
EXTENSIONS
More terms from Robert G. Wilson v, Feb 20 2004
STATUS
approved