A035930 - OEIS

%I #31 Oct 05 2021 22:00:42

%S 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,

%T 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,

%U 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

%N Maximal product of any two numbers whose concatenation is n.

%C 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

%H Alois P. Heinz, <a href="/A035930/b035930.txt">Table of n, a(n) for n = 0..9999</a>

%H Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2021/08/surface-of-number.html">Surface of a number</a>, Sep 01 2021.

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

%p a:= proc(n) local l, m; l:= convert(n, base, 10); m:= nops(l);

%p       `if`(m<2, 0, max(seq(parse(cat(seq(l[m-i], i=0..j-1)))

%p        *parse(cat(seq(l[m-i], i=j..m-1))), j=1..m)))

%p     end:

%p seq(a(n), n=0..120);  # _Alois P. Heinz_, May 22 2009

%t Flatten[With[{c=Range[0,9]},Table[c*n,{n,0,10}]]] (* _Harvey P. Dale_, Jun 07 2012 *)

%o (Haskell)

%o a035930 n | n < 10    = 0

%o           | otherwise = maximum $ zipWith (*)

%o             (map read $ init $ tail $ inits $ show n)

%o             (map read $ tail $ init $ tails $ show n)

%o -- _Reinhard Zumkeller_, Aug 14 2011

%o (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

%o (Python)

%o def a(n):

%o     s = str(n)

%o     return max((int(s[:i])*int(s[i:]) for i in range(1, len(s))), default=0)

%o print([a(n) for n in range(108)]) # _Michael S. Branicky_, Sep 01 2021

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

%K nonn,base,nice,look

%O 0,13

%A _Erich Friedman_

%E An erroneous formula was deleted by _N. J. A. Sloane_, Dec 23 2008