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%I #12 Jun 27 2013 03:25:58
%S 0,0,1,0,2,2,3,0,4,4,6,4,6,6,9,0,8,8,12,8,10,12,15,8,12,12,18,12,15,
%T 18,21,0,16,16,24,16,20,24,28,16,20,20,30,24,26,30,35,16,24,24,36,24,
%U 30,36,42,24,28,30,42,36,39,42,49,0,32,32,48,32,40,48,56,32,36,40,54
%N Maximum of the products of left and right parts when splitting the binary representation of n.
%C a(2^n) = 0, a(2^n + 1) = 2^(n-1).
%C a(2*n+1) > a(2*n) = 2*a(n). - _Reinhard Zumkeller_, Jun 27 2013
%H Reinhard Zumkeller, <a href="/A088864/b088864.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(n) = Max{floor(n/(2^k))*(n mod 2^k)}.
%e n=77 -> '1001101': a(77) = Max{'1'*'001101', '10'*'01101',
%e '100'*'1101', '1001'*'101', '10011'*'01', '100110'*'1'} = Max{1*13, 2*13,
%e 4*13, 9*5, 19*1, 38*1} = Max{13, 26, 52, 45, 19, 38} = 52.
%t mplrp[n_]:=Module[{idn2=IntegerDigits[n,2],len},len=Length[idn2];Max[ Times @@@Table[{FromDigits[Take[idn2,i],2],FromDigits[Take[ idn2, -(len-i)],2]},{i,len}]]]; Array[mplrp,80] (* _Harvey P. Dale_, Jun 24 2013 *)
%o (Haskell)
%o import Data.List (inits, tails)
%o import Data.Function (on)
%o a088864 1 = 0
%o a088864 n = maximum $ zipWith ((*) `on` foldr (\d v -> v * 2 + d) 0)
%o (init $ tail $ inits bs) (init $ tail $ tails bs)
%o where bs = a030308_row n
%o -- _Reinhard Zumkeller_, Jun 27 2013
%Y Cf. A007088.
%Y Cf. A030308.
%K nonn,base
%O 1,5
%A _Reinhard Zumkeller_, Nov 26 2003
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