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A066196
Primes which have an equal number of zeros and ones in their binary expansion.
12
2, 37, 41, 139, 149, 163, 197, 541, 557, 563, 569, 587, 601, 613, 617, 647, 653, 659, 661, 677, 709, 787, 809, 929, 2141, 2203, 2221, 2251, 2281, 2333, 2347, 2357, 2381, 2389, 2393, 2417, 2467, 2473, 2617, 2659, 2699, 2707, 2713, 2729, 2837, 2851, 2857
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
FORMULA
A000040 INTERSECT A031443. - R. J. Mathar, Jun 01 2011
MATHEMATICA
Prime[ Select[ Range[ 10^3 ], Count[ IntegerDigits[ Prime[ # ], 2 ], 0 ] == Count[ IntegerDigits[ Prime[ # ], 2 ], 1 ] & ] ]
digBalQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ@(m = Length@d) && Count[d, 1] == m/2]; Select[Range[3000], PrimeQ[#] && digBalQ[#] &] (* Amiram Eldar, Nov 21 2020 *)
PROG
(PARI) isok(p) = isprime(p) && (2*hammingweight(p) == #binary(p)); \\ Michel Marcus, May 16 2022
(Python)
from itertools import count, islice
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def agen():
yield from filter(isprime, (int("1"+"".join(p), 2) for n in count(1) for p in multiset_permutations("0"*n+"1"*(n-1))))
print(list(islice(agen(), 50))) # Michael S. Branicky, May 15 2022
CROSSREFS
Sequence in context: A375171 A290803 A042569 * A107180 A162577 A199980
KEYWORD
nonn,base
AUTHOR
Robert G. Wilson v, Dec 15 2001
STATUS
approved