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A088864 Maximum of the products of left and right parts when splitting the binary representation of n. 1
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, 18, 21, 0, 16, 16, 24, 16, 20, 24, 28, 16, 20, 20, 30, 24, 26, 30, 35, 16, 24, 24, 36, 24, 30, 36, 42, 24, 28, 30, 42, 36, 39, 42, 49, 0, 32, 32, 48, 32, 40, 48, 56, 32, 36, 40, 54 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(2^n) = 0, a(2^n + 1) = 2^(n-1).

a(2*n+1) > a(2*n) = 2*a(n). - Reinhard Zumkeller, Jun 27 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = Max{floor(n/(2^k))*(n mod 2^k)}.

EXAMPLE

n=77 -> '1001101': a(77) = Max{'1'*'001101', '10'*'01101',

'100'*'1101', '1001'*'101', '10011'*'01', '100110'*'1'} = Max{1*13, 2*13,

4*13, 9*5, 19*1, 38*1} = Max{13, 26, 52, 45, 19, 38} = 52.

MATHEMATICA

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 *)

PROG

(Haskell)

import Data.List (inits, tails)

import Data.Function (on)

a088864 1 = 0

a088864 n = maximum $ zipWith ((*) `on` foldr (\d v -> v * 2 + d) 0)

            (init $ tail $ inits bs) (init $ tail $ tails bs)

            where bs = a030308_row n

-- Reinhard Zumkeller, Jun 27 2013

CROSSREFS

Cf. A007088.

Cf. A030308.

Sequence in context: A104594 A079626 A257697 * A330925 A191361 A199784

Adjacent sequences:  A088861 A088862 A088863 * A088865 A088866 A088867

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Nov 26 2003

STATUS

approved

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)