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A343258
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Numbers whose binary representation has a prime number of zeros and a prime number of ones.
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1
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9, 10, 12, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 65, 66, 68, 72, 79, 80, 87, 91, 93, 94, 96, 103, 107, 109, 110, 115, 117, 118, 121, 122, 124, 131, 133, 134, 137, 138, 140, 143, 145, 146, 148, 151, 152, 155, 157, 158
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OFFSET
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1,1
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COMMENTS
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Terms of 4, 5 and 6 total bits (9 through 56) are the same as A089648.
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LINKS
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MAPLE
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q:= n->(l->(t->andmap(isprime, [t, nops(l)-t]))(add(i, i=l)))(Bits[Split](n)):
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MATHEMATICA
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Select[Range[160], And @@ PrimeQ[DigitCount[#, 2]] &] (* Amiram Eldar, Apr 09 2021 *)
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PROG
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(PARI)
isa(n)= isprime(hammingweight(n));
isb(n)= isprime(#binary(n) - hammingweight(n));
isok(n) = isa(n) && isb(n);
(Python)
from sympy import isprime
def ok(n): b = bin(n)[2:]; return all(isprime(b.count(d)) for d in "01")
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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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