A080941 Greatest 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, 3, 0, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 3, 4, 1, 6, 1, 0, 1, 2, 1, 4, 1, 2, 3, 8, 1, 2, 1, 4, 5, 2, 1, 16, 1, 2, 3, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 7, 0, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 3, 4, 1, 6, 1, 16, 1, 2, 1, 4, 5, 2, 3, 8, 1, 10, 1, 4, 1, 2, 1, 32, 1, 2, 3, 4, 1, 6, 1

Offset: 1

Author

Reinhard Zumkeller, Feb 25 2003

Keywords

• nonn
• base

Comments

a(n)=0 iff n=2^k (A000079);

Examples

			n=30='11110', divisors<30: 1='1', 2='10', 3='11', 5='101', 6='110', 10='1010' and 15='1111', therefore a(30)=2='10';
n=31='11111', divisors<31: 1='1', therefore a(31)=1;
n=32='100000', divisors<32: 1='1', 2='10', 4='100', 8='1000' and 16='10000', therefore a(32)=0.
		

Links

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

Crossrefs

Cf. A007088, A080940, A080942.

Cf. A030308, A027751.

Programs

Haskell

import Data.List (isPrefixOf); import Data.Function (on)
a080941 n = if null ds then 0 else head ds  where
            ds = filter ((flip isPrefixOf `on` a030308_row) n) $
                        reverse $ a027751_row n
-- Reinhard Zumkeller, Mar 27 2014

Extensions

Definition improved by Reinhard Zumkeller, Mar 27 2014