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A345867
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Total number of 0's in the binary expansions of the first n primes.
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2
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1, 1, 2, 2, 3, 4, 7, 9, 10, 11, 11, 14, 17, 19, 20, 22, 23, 24, 28, 31, 35, 37, 40, 43, 47, 50, 52, 54, 56, 59, 59, 64, 69, 73, 77, 80, 83, 87, 90, 93, 96, 99, 100, 105, 109, 112, 115, 116, 119, 122, 125, 126, 129, 130, 137, 142, 147, 151, 156, 161, 165, 170
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = a(n-1) for n in { A059305 }.
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EXAMPLE
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a(3) = 2: 2 = 10_2, 3 = 11_2, 5 = 101_2, so there are two 0's in the binary expansions of the first three primes.
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 0, a(n-1)
+add(1-i, i=Bits[Split](ithprime(n))))
end:
seq(a(n), n=1..100);
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MATHEMATICA
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Accumulate[DigitCount[Prime[Range[100]], 2, 0]] (* Paolo Xausa, Feb 26 2024 *)
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PROG
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(Python)
from sympy import prime, primerange
from itertools import accumulate
def f(n): return (bin(n)[2:]).count('0')
def aupton(nn): return list(accumulate(map(f, primerange(2, prime(nn)+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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