A261891 Least k>0 such that n AND (k*n) = 0, where AND stands for the binary AND operator.

2, 2, 4, 2, 2, 4, 8, 2, 2, 2, 12, 4, 10, 8, 16, 2, 2, 2, 4, 2, 2, 12, 24, 4, 4, 10, 12, 8, 10, 16, 32, 2, 2, 2, 4, 2, 2, 4, 40, 2, 2, 2, 12, 12, 10, 24, 48, 4, 4, 4, 4, 10, 34, 12, 56, 8, 18, 10, 12, 16, 42, 32, 64, 2, 2, 2, 4, 2, 2, 4, 8, 2, 2, 2, 12, 4, 10

Offset: 1

Author

Paul Tek, Sep 05 2015

Keywords

• nonn
• base
• look

Comments

All terms are even.

a(A003714(n)) = 2 for any n>0.

a(A004780(n)) > 2 for any n>0.

a(n) <= 2^A116361(n) for any n>0.

a(2n) = a(n) for any n>0.

Examples

			For n=7:
+---+-------------+
| k | 7 AND (k*7) |
|   | (in binary) |
+---+-------------+
| 1 |         111 |
| 2 |         110 |
| 3 |         101 |
| 4 |         100 |
| 5 |          11 |
| 6 |          10 |
| 7 |           1 |
| 8 |           0 |
+---+-------------+
Hence, a(7) = 8.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A003714, A004780, A116361, A261892.

Programs

Mathematica

Table[k = 1; While[BitAnd[k n, n] != 0, k++]; k, {n, 60}] (* Michael De Vlieger, Sep 06 2015 *)

PARI

a(n) = {k=1; while (bitand(n, k*n), k++); k;} \\ Michel Marcus, Sep 06 2015

Perl

sub a {
   my $n = shift;
   my $k = 1;
   while ($n & ($k*$n)) {
      $k++;
   }
   return $k;
}

Python

from itertools import count
def A261891(n): return next(k for k in count(2) if not n&k*n) # Chai Wah Wu, Jul 19 2024