A102212 -id:A102212 - cp's OEIS frontend

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

Reinhard Zumkeller, Dec 30 2004

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

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

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

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

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

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

A102211 Numbers k with A102210(k) = 0.

Original entry on oeis.org

1, 4, 8, 9, 12, 16, 20, 24, 28, 32, 33, 36, 40, 44, 48, 52, 56, 60, 64, 65, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 129, 132, 136, 140, 144, 148, 152, 156, 160, 161, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216

Offset: 1

Reinhard Zumkeller, Dec 30 2004

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

A008586 is a subsequence.

Cf. A102210, A102212, A102213.

[k:k in [1..220]|#[p:p in PrimesUpTo(k)| p eq BitwiseAnd(k,p)] eq 0 ]; // Marius A. Burtea, Jan 12 2020

f[n_] := Count[Range[n], ?(PrimeQ[#] && BitAnd[n, #] == # &)]; Select[Range[216], f[#] == 0 &] (* _Amiram Eldar, Jan 12 2020 *)

A102210(a(n)) = 0.

A102213 Numbers m with A102210(m) > 1.

Original entry on oeis.org

3, 7, 11, 13, 15, 19, 21, 23, 27, 29, 31, 35, 37, 39, 43, 45, 47, 51, 53, 55, 57, 59, 61, 63, 67, 71, 75, 77, 79, 83, 85, 87, 89, 91, 93, 95, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 131, 135, 139, 141, 143, 147, 149, 151, 153, 155, 157

Offset: 1

Reinhard Zumkeller, Dec 30 2004

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

Subsequence of A005408.

Cf. A102210, A102211, A102212.

[k:k in [1..160]|#[p:p in PrimesUpTo(k)| p eq BitwiseAnd(k,p)] gt 1 ]; // Marius A. Burtea, Jan 12 2020

f[n_] := Count[Range[n], ?(PrimeQ[#] && BitAnd[n, #] == # &)]; Select[Range[216], f[#] > 1 &] (* _Amiram Eldar, Jan 12 2020 *)

A102210(a(n)) > 1.

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A102210 Number of primes that are bitwise covered by n.

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A102211 Numbers k with A102210(k) = 0.

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A102213 Numbers m with A102210(m) > 1.

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