A078834 Greatest prime factor of n also contained as binary substring in binary representation of n; a(n)=1, if no such factor exists.

1, 2, 3, 2, 5, 3, 7, 2, 1, 5, 11, 3, 13, 7, 3, 2, 17, 2, 19, 5, 1, 11, 23, 3, 1, 13, 3, 7, 29, 3, 31, 2, 1, 17, 1, 2, 37, 19, 3, 5, 41, 2, 43, 11, 5, 23, 47, 3, 1, 2, 3, 13, 53, 3, 11, 7, 3, 29, 59, 3, 61, 31, 7, 2, 1, 2, 67, 17, 1, 2, 71, 2, 73, 37, 5, 19, 1, 3, 79, 5, 1, 41, 83, 2, 5, 43

Offset: 1

Author

Reinhard Zumkeller, Dec 08 2002

Keywords

• nonn
• base
• nice

Comments

a(n) <= min{A078833(n), A006530(n)};

for n>1: a(n) = n iff n is prime.

a(A100484(n)) = A000040(n); a(A100368(n)) = A006530(A100368(n)). [Reinhard Zumkeller, Sep 19 2011]

Examples

			n=15=3*5 has two factors; only '11'=3 is contained in '1111'=15, therefore a(15)=3.
		

Links

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

Crossrefs

Cf. A078833, A078822, A007088, A006530.

Programs

Haskell

import Numeric (showIntAtBase)
import Data.List (find, isInfixOf)
import Data.Maybe (fromMaybe)
a078834 n = fromMaybe 1 $ find (\p -> showIntAtBase 2 ("01" !!) p ""
                          `isInfixOf` showIntAtBase 2 ("01" !!) n "") $
                 reverse $ a027748_row n
-- Reinhard Zumkeller, Sep 19 2011

Mathematica

a[n_] := Module[{bn, pp, sel}, bn = IntegerDigits[n, 2]; pp = FactorInteger[n][[All, 1]]; sel = Select[pp, MatchQ[bn, {_, Sequence @@ IntegerDigits[#, 2], _}] &]; If[sel == {}, 1, Max[sel]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Aug 13 2013 *)