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A066196
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Primes which have an equal number of zeros and ones in their binary expansion.
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10
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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MATHEMATICA
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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 *)
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PROG
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(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))))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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