A261891 - OEIS

%I #22 Jul 19 2024 19:08:45

%S 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,

%T 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,

%U 12,16,42,32,64,2,2,2,4,2,2,4,8,2,2,2,12,4,10

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

%C All terms are even.

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

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

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

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

%H Paul Tek, <a href="/A261891/b261891.txt">Table of n, a(n) for n = 1..16384</a>

%e For n=7:

%e +---+-------------+

%e | k | 7 AND (k*7) |

%e |   | (in binary) |

%e +---+-------------+

%e | 1 |         111 |

%e | 2 |         110 |

%e | 3 |         101 |

%e | 4 |         100 |

%e | 5 |          11 |

%e | 6 |          10 |

%e | 7 |           1 |

%e | 8 |           0 |

%e +---+-------------+

%e Hence, a(7) = 8.

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

%o (Perl) sub a {

%o    my $n = shift;

%o    my $k = 1;

%o    while ($n & ($k*$n)) {

%o       $k++;

%o    }

%o    return $k;

%o }

%o (PARI) a(n) = {k=1; while (bitand(n, k*n), k++); k;} \\ _Michel Marcus_, Sep 06 2015

%o (Python)

%o from itertools import count

%o def A261891(n): return next(k for k in count(2) if not n&k*n) # _Chai Wah Wu_, Jul 19 2024

%Y Cf. A003714, A004780, A116361, A261892.

%K nonn,base,look

%O 1,1

%A _Paul Tek_, Sep 05 2015