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

0,13

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..9999

Eric Angelini, Surface of a number, Sep 01 2021.

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A080464 A171765 A257297 * A347470 A088117 A349278

Adjacent sequences: A035927 A035928 A035929 * A035931 A035932 A035933

Keyword

nonn,base,nice,look

Author

Erich Friedman

Extensions

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

Status

approved