A102210 -id:A102210 - cp's OEIS frontend

A102211 Numbers k with A102210(k) = 0.

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.

A102212 Numbers m with A102210(m) = 1.

Original entry on oeis.org

2, 5, 6, 10, 14, 17, 18, 22, 25, 26, 30, 34, 38, 41, 42, 46, 49, 50, 54, 58, 62, 66, 69, 70, 73, 74, 78, 81, 82, 86, 90, 94, 97, 98, 102, 106, 110, 114, 118, 122, 126, 130, 133, 134, 137, 138, 142, 145, 146, 150, 154, 158, 162, 166, 170, 174, 177, 178, 182, 186, 190

Offset: 1

Reinhard Zumkeller, Dec 30 2004

;

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

A016825 is a subsequence.

Cf. A102210, A102211, A102213.

[k:k in [1..200]|#[p:p in PrimesUpTo(k)| p eq BitwiseAnd(k,p)] eq 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.

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.

A102550 Number of distinct prime-factors of n that are bitwise covered by n.

Original entry on oeis.org

0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 1, 0, 1, 1, 0, 0, 0, 1, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0

Offset: 1

Reinhard Zumkeller, Jan 14 2005

nonn

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

Index entries for sequences related to binary expansion of n

Cf. A001221 (omega), A007088, A004676, A080099, A102210.

Cf. A102551, A102553, A102554, A102555.

a[1] = 0; a[k_] := Module[{f=FactorInteger[k][[;; , 1]]}, Count[BitAnd[k, f]-f, 0]];  Array[a,120] (* Amiram Eldar, Feb 06 2019 *)

a(A102553(n)) = A001221(A102553(n));
a(A102554(n)) < A001221(A102554(n));
a(A102551(n)) = 0, a(A102551(n)) > 0;
a(A102555(n)) = n;
a(m) < n for m < A102555(n).
a(n) = Sum_{p|n} (binomial(n,p) mod 2), where p is a prime. - Ridouane Oudra, May 03 2019

Offset 1 from Amiram Eldar, Feb 06 2019

A375487 a(n) is the number of integers k between 0 and n such that n AND k is a prime number (where AND denotes the bitwise AND operator).

Original entry on oeis.org

0, 0, 1, 2, 0, 1, 2, 4, 0, 0, 4, 5, 0, 3, 2, 6, 0, 1, 8, 10, 0, 6, 4, 11, 0, 4, 4, 10, 0, 7, 2, 11, 0, 0, 16, 16, 0, 9, 8, 17, 0, 1, 8, 14, 0, 12, 4, 16, 0, 8, 8, 16, 0, 13, 4, 17, 0, 8, 4, 15, 0, 15, 2, 18, 0, 0, 32, 33, 0, 16, 16, 34, 0, 1, 16, 27, 0, 18, 8

Offset: 0

Rémy Sigrist, Aug 17 2024

			The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  ------------------
   0     0  None
   1     0  None
   2     1  2
   3     2  2, 3
   4     0  None
   5     1  5
   6     2  2, 3
   7     4  2, 3, 5, 7
   8     0  None
   9     0  None
  10     4  2, 3, 6, 7
  11     5  2, 3, 6, 7, 11
  12     0  None
  13     3  5, 7, 13
  14     2  2, 3
  15     6  2, 3, 5, 7, 11, 13

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Rémy Sigrist, Scatterplot of (n, k) such that 0 <= k <= n <= 1024 and n AND k is prime

Cf. A000720, A102210, A117494, A375485 (XOR variant), A375486 (OR variant).

a(n) = sum(k = 0, n, isprime(bitand(n, k)))

a(n) = 0 iff n = 0 or n belongs to A102210.

a(2^k-1) = A000720(2^k-1) for any k > 0.

cp's OEIS Frontend

A102211 Numbers k with A102210(k) = 0.

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A102212 Numbers m with A102210(m) = 1.

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A102213 Numbers m with A102210(m) > 1.

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A102550 Number of distinct prime-factors of n that are bitwise covered by n.

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A375487 a(n) is the number of integers k between 0 and n such that n AND k is a prime number (where AND denotes the bitwise AND operator).

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