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

Author

Reinhard Zumkeller, Feb 25 2003

Keywords

• nonn
• base
• easy

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).

Also, the first repeating value of the periodic sequences created by 2^k mod n. - Alison J. McCrea, Apr 13 2025

Examples

			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.
		

Links

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

Crossrefs

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

Cf. A030308, A027751.

Programs

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

Extensions

Definition improved by Reinhard Zumkeller, Mar 27 2014