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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

(Perl) sub a {
   my $n = shift;
   my $k = 1;
   while ($n & ($k*$n)) {
      $k++;
   }
   return $k;
}
(PARI) a(n) = {k=1; while (bitand(n, k*n), k++); k; } \\ Michel Marcus, Sep 06 2015
(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

Crossrefs

Cf. A003714, A004780, A116361, A261892.

Sequence in context: A064145 A213431 A331985 * A321320 A366808 A175462

Adjacent sequences: A261888 A261889 A261890 * A261892 A261893 A261894

Keyword

nonn,base,look

Author

Paul Tek, Sep 05 2015

Status

approved