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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.

%I A078834 #19 Feb 23 2024 07:25:48
%S A078834 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,
%T A078834 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,
%U A078834 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
%N A078834 Greatest prime factor of n also contained as binary substring in binary representation of n; a(n)=1, if no such factor exists.
%C A078834 a(n) <= min{A078833(n), A006530(n)};
%C A078834 for n>1: a(n) = n iff n is prime.
%C A078834 a(A100484(n)) = A000040(n); a(A100368(n)) = A006530(A100368(n)). [_Reinhard Zumkeller_, Sep 19 2011]
%H A078834 Reinhard Zumkeller, <a href="/A078834/b078834.txt">Table of n, a(n) for n = 1..10000</a>
%e A078834 n=15=3*5 has two factors; only '11'=3 is contained in '1111'=15, therefore a(15)=3.
%t A078834 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 *)
%o A078834 (Haskell)
%o A078834 import Numeric (showIntAtBase)
%o A078834 import Data.List (find, isInfixOf)
%o A078834 import Data.Maybe (fromMaybe)
%o A078834 a078834 n = fromMaybe 1 $ find (\p -> showIntAtBase 2 ("01" !!) p ""
%o A078834                           `isInfixOf` showIntAtBase 2 ("01" !!) n "") $
%o A078834                  reverse $ a027748_row n
%o A078834 -- _Reinhard Zumkeller_, Sep 19 2011
%Y A078834 Cf. A078833, A078822, A007088, A006530.
%K A078834 nonn,base,nice
%O A078834 1,2
%A A078834 _Reinhard Zumkeller_, Dec 08 2002