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A343258
Numbers whose binary representation has a prime number of zeros and a prime number of ones.
1
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
OFFSET
1,1
COMMENTS
Terms of 4, 5 and 6 total bits (9 through 56) are the same as A089648.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 78 terms from Jean-Jacques Vaudroz)
MAPLE
q:= n->(l->(t->andmap(isprime, [t, nops(l)-t]))(add(i, i=l)))(Bits[Split](n)):
select(q, [$1..200])[]; # Alois P. Heinz, Apr 11 2021
MATHEMATICA
Select[Range[160], And @@ PrimeQ[DigitCount[#, 2]] &] (* Amiram Eldar, Apr 09 2021 *)
PROG
(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")
print(list(filter(ok, range(159)))) # Michael S. Branicky, Sep 10 2021
CROSSREFS
Intersection of A052294 and A144754.
Cf. A089648.
Sequence in context: A242475 A160947 A158581 * A078459 A156345 A078390
KEYWORD
nonn,base
AUTHOR
STATUS
approved