A102210 Number of primes that are bitwise covered by n.

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

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

Crossrefs

Cf. A007053, A007088, A004676, A080099, A102211, A102212, A102213, A102550.

Sequence in context: A333158 A293135 A321376 * A124220 A221755 A354666

Adjacent sequences: A102207 A102208 A102209 * A102211 A102212 A102213

Keyword

nonn,base

Author

Reinhard Zumkeller, Dec 30 2004

Status

approved