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

Author

Reinhard Zumkeller, Dec 30 2004

Keywords

• nonn
• base

Comments

p is bitwise covered by n iff (p = (n AND p)) bitwise: A080099(n,p)=p.

Examples

			n=21->10101 -> a(21) = #{00101=5,10001=17} = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

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

Programs

Magma

[#[p:p in PrimesUpTo(n)| p eq BitwiseAnd(n,p)] :n in [1..105] ]; // Marius A. Burtea, Jan 12 2020

Mathematica

a[n_] := Count[Range[n], ?(PrimeQ[#] && BitAnd[n, #] == # &)]; Array[a, 100] (* _Amiram Eldar, Jan 12 2020 *)

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