A035930 Maximal product of any two numbers whose concatenation is n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 10, 20, 30, 40, 50, 60, 70

Offset: 0

Author

Erich Friedman

Keywords

• nonn
• base
• nice
• look

Comments

Agrees up to a(100) = 0 with A088117, A171765 and A257297, but all of the four differ in a(101) and subsequent values. - M. F. Hasler, Sep 01 2021

Examples

			a(341) = max(34*1,3*41) = 123.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..9999
• Eric Angelini, Surface of a number, Sep 01 2021.

Crossrefs

Different from A007954, A088117, A171765 and A257297. Cf. A035931-A035935.

Programs

Haskell

a035930 n | n < 10    = 0
          | otherwise = maximum $ zipWith (*)
            (map read $ init $ tail $ inits $ show n)
            (map read $ tail $ init $ tails $ show n)
-- Reinhard Zumkeller, Aug 14 2011

Maple

a:= proc(n) local l, m; l:= convert(n, base, 10); m:= nops(l);
      `if`(m<2, 0, max(seq(parse(cat(seq(l[m-i], i=0..j-1)))
       *parse(cat(seq(l[m-i], i=j..m-1))), j=1..m)))
    end:
seq(a(n), n=0..120);  # Alois P. Heinz, May 22 2009

Mathematica

Flatten[With[{c=Range[0,9]},Table[c*n,{n,0,10}]]] (* Harvey P. Dale, Jun 07 2012 *)

PARI

apply( {A035930(n)=if(n>9,vecmax([vecprod(divrem( n,10^j))|j<-[1..logint(n,10)]]))}, [0..111]) \\ M. F. Hasler, Sep 01 2021

Python

def a(n):
    s = str(n)
    return max((int(s[:i])*int(s[i:]) for i in range(1, len(s))), default=0)
print([a(n) for n in range(108)]) # Michael S. Branicky, Sep 01 2021

Extensions

An erroneous formula was deleted by N. J. A. Sloane, Dec 23 2008