A080940 Smallest proper divisor of n which is a suffix of n in binary representation; a(n) = 0 if no such divisor exists.

0, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 4, 1, 2, 1, 0, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 0, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 0, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 32, 1, 2, 1, 4, 1, 2, 1, 8

Offset

1,6

Comments

By definition, identical to A006519 except that a(2^k) = 0 for all k.

a(3*2^k)=2^k and a(m)<2^k for m<3*2^k (see A007283).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

n=6='110', divisors<6: 1='1', 2='10' and 3='11', therefore a(6)=2='10';
n=7='111', divisors<7: 1='1', therefore a(7)=1;
n=8='1000', divisors<8: 1='1', 2='10' and 4='100', therefore a(8)=0.

Prog

(Haskell)
import Data.List (isPrefixOf); import Data.Function (on)
a080940 n = if null ds then 0 else head ds  where
            ds = filter ((flip isPrefixOf `on` a030308_row) n) $
                        a027751_row n
-- Reinhard Zumkeller, Mar 27 2014
(Python)
def A080940(n): return (m:=n&-n)*(m!=n) # Chai Wah Wu, Jun 20 2023

Crossrefs

Cf. A007088, A000079, A080941, A080942, A006519.

Cf. A030308, A027751.

Sequence in context: A335511 A345221 A346633 * A080941 A346705 A177405

Adjacent sequences: A080937 A080938 A080939 * A080941 A080942 A080943

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Feb 25 2003

Extensions

Definition improved by Reinhard Zumkeller, Mar 27 2014

Status

approved