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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

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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