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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.
3
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
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
KEYWORD
nonn,base,nice
AUTHOR
Reinhard Zumkeller, Dec 08 2002
STATUS
approved