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%I #29 May 16 2022 09:59:59
%S 2,37,41,139,149,163,197,541,557,563,569,587,601,613,617,647,653,659,
%T 661,677,709,787,809,929,2141,2203,2221,2251,2281,2333,2347,2357,2381,
%U 2389,2393,2417,2467,2473,2617,2659,2699,2707,2713,2729,2837,2851,2857
%N Primes which have an equal number of zeros and ones in their binary expansion.
%H Amiram Eldar, <a href="/A066196/b066196.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%F A000040 INTERSECT A031443. - _R. J. Mathar_, Jun 01 2011
%t Prime[ Select[ Range[ 10^3 ], Count[ IntegerDigits[ Prime[ # ], 2 ], 0 ] == Count[ IntegerDigits[ Prime[ # ], 2 ], 1 ] & ] ]
%t 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 *)
%o (PARI) isok(p) = isprime(p) && (2*hammingweight(p) == #binary(p)); \\ _Michel Marcus_, May 16 2022
%o (Python)
%o from itertools import count, islice
%o from sympy import isprime
%o from sympy.utilities.iterables import multiset_permutations
%o def agen():
%o yield from filter(isprime, (int("1"+"".join(p), 2) for n in count(1) for p in multiset_permutations("0"*n+"1"*(n-1))))
%o print(list(islice(agen(), 50))) # _Michael S. Branicky_, May 15 2022
%Y Cf. A000040, A031443.
%K nonn,base
%O 1,1
%A _Robert G. Wilson v_, Dec 15 2001
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