A078834 - OEIS

%I #19 Feb 23 2024 07:25:48

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

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

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

%C a(A100484(n)) = A000040(n); a(A100368(n)) = A006530(A100368(n)). [_Reinhard Zumkeller_, Sep 19 2011]

%H Reinhard Zumkeller, <a href="/A078834/b078834.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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 (Haskell)

%o import Numeric (showIntAtBase)

%o import Data.List (find, isInfixOf)

%o import Data.Maybe (fromMaybe)

%o a078834 n = fromMaybe 1 $ find (\p -> showIntAtBase 2 ("01" !!) p ""

%o                           `isInfixOf` showIntAtBase 2 ("01" !!) n "") $

%o                  reverse $ a027748_row n

%o -- _Reinhard Zumkeller_, Sep 19 2011

%Y Cf. A078833, A078822, A007088, A006530.

%K nonn,base,nice

%O 1,2

%A _Reinhard Zumkeller_, Dec 08 2002