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A102210
Number of primes that are bitwise covered by n.
6
0, 1, 2, 0, 1, 1, 4, 0, 0, 1, 3, 0, 2, 1, 6, 0, 1, 1, 4, 0, 2, 1, 7, 0, 1, 1, 5, 0, 4, 1, 11, 0, 0, 1, 2, 0, 2, 1, 5, 0, 1, 1, 5, 0, 4, 1, 10, 0, 1, 1, 4, 0, 4, 1, 9, 0, 2, 1, 8, 0, 8, 1, 18, 0, 0, 1, 3, 0, 1, 1, 6, 0, 1, 1, 5, 0, 3, 1, 10, 0, 1, 1, 6, 0, 2, 1, 10, 0, 3, 1, 9, 0, 6, 1, 17, 0, 1, 1, 4, 0, 4, 1
OFFSET
1,3
COMMENTS
p is bitwise covered by n iff (p = (n AND p)) bitwise: A080099(n,p)=p.
FORMULA
a(A102211(n)) = 0; a(A102212(n)) = 1; a(A102213(n)) > 1.
a(2^k-1) = A007053(k) for k > 1. - Amiram Eldar, Jan 12 2020
EXAMPLE
n=21->10101 -> a(21) = #{00101=5,10001=17} = 2.
MATHEMATICA
a[n_] := Count[Range[n], _?(PrimeQ[#] && BitAnd[n, #] == # &)]; Array[a, 100] (* Amiram Eldar, Jan 12 2020 *)
PROG
(Magma) [#[p:p in PrimesUpTo(n)| p eq BitwiseAnd(n, p)] :n in [1..105] ]; // Marius A. Burtea, Jan 12 2020
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Dec 30 2004
STATUS
approved