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

1,2

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]

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A078833, A078822, A007088, A006530.

Sequence in context: A097975 A130088 A369033 * A039634 A078833 A210437

Adjacent sequences: A078831 A078832 A078833 * A078835 A078836 A078837

Keyword

nonn,base,nice

Author

Reinhard Zumkeller, Dec 08 2002

Status

approved