A035935 -id:A035935 - cp's OEIS frontend

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

Erich Friedman

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

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

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

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

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

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

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

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

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

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

A035931 Number of steps to reach 0 under "k->max product of two numbers whose concatenation is k".

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 1, 2, 2, 3, 3, 2, 3, 4, 3, 4, 1, 2, 2, 3, 2, 3, 2, 4, 2, 3, 1, 2, 3, 3, 3, 2, 4, 3, 4, 3, 1, 2, 3, 3, 4, 4, 3, 5, 3, 4, 1, 2, 3, 3, 3, 2, 4, 3, 4, 4, 1, 2, 3, 4, 4, 3, 3, 4, 4, 3, 1

Offset: 0

Erich Friedman

			a(341)=5 since 341->123->36->18->8->0.

Scott R. Shannon, Table of n, a(n) for n = 0..10000.

Cf. A035930, A035932, A035933, A035934, A035935.

f[n_] := If[n<10, 0, With[{d = IntegerDigits[n]}, Table[FromDigits[Take[d, k]]*FromDigits[Drop[d, k]], {k, 1, Length[d]-1}] // Max]];
a[n_] := If[n == 0, 0, Length[FixedPointList[f, n]]-2];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 03 2017 *)

A035934 Smallest number that can be made to take n steps to reach 0 under "k -> any product of 2 numbers whose concatenation is k".

Original entry on oeis.org

0, 1, 11, 26, 39, 77, 117, 139, 429, 529, 777, 1117, 1669, 2238, 2993, 3697, 4779, 5319, 5919, 10998, 11794, 14989, 21179, 26869, 27797, 36177, 38993, 62958, 74297, 85797, 95339, 113319, 125919, 139919, 199683, 201799, 247817, 333329, 360497, 419926

Offset: 0

Erich Friedman

			a(6) = 117 since 117 -> 77 -> 49 -> 36 -> 18 -> 8 -> 0.

Cf. A035930-A035935.

tbl=Table[1, {10}]; Do[tbl=Append[tbl, b=IntegerDigits[k]; If[(First[b]==0||Last[b]==0), 1, Max[Part[tbl, Table[FromDigits[Take[b, i]]*FromDigits[Take[b, i-Length[b]]], {i, 1, Length[b]-1}]]]+1]], {k, 11, 170000}]; tbl; m=Max[tbl]; Prepend[Flatten[Table[Position[tbl, i, 1, 1], {i, 1, m}]], 0]

More terms from Naohiro Nomoto, Apr 11 2001
More terms from Vit Planocka (planocka(AT)mistral.cz), Feb 01 2003
More terms from Martin Fuller, Jun 02 2006

A035932 Smallest number that takes n steps to reach 0 under "k->max product of 2 numbers whose concatenation is k".

Original entry on oeis.org

0, 1, 11, 26, 39, 77, 117, 139, 449, 529, 777, 1117, 2229, 2982, 4267, 4779, 5319, 5919, 8693, 12699, 14119, 17907, 27779, 47877, 80299, 103199, 135199, 274834, 293938, 312794, 606963, 653993, 773989, 1160892, 1296741, 1616696, 1986576

Offset: 0

Erich Friedman

Giovanni Resta, Table of n, a(n) for n = 0..100 (terms 0..50 from Scott R. Shannon)
Scott R. Shannon, The 50 steps to 0 for start value n = 74438327.

Cf. A035930, A035931, A035933, A035934, A035935.

More terms from Naohiro Nomoto, Apr 03 2001

A035933 Smallest number that takes n steps to reach 0 under "k->min product of 2 numbers whose concatenation is k".

Original entry on oeis.org

0, 1, 11, 26, 39, 77, 177, 359, 977, 1977, 3659, 13659, 28879, 128879, 289978, 999663, 4474997, 14474997, 39596964, 139596964, 389999999, 1389999999, 2899999999, 12899999999, 49999999986, 149999999986, 446874999996, 1446874999996

Offset: 0

Erich Friedman

a(28) > 4.4*10^12. - Jon E. Schoenfield, Jan 05 2009

Cf. A035930-A035935.

More terms from Naohiro Nomoto, Apr 03 2001

a(18)-a(27) from Jon E. Schoenfield, Jan 05 2009

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

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A035931 Number of steps to reach 0 under "k->max product of two numbers whose concatenation is k".

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A035934 Smallest number that can be made to take n steps to reach 0 under "k -> any product of 2 numbers whose concatenation is k".

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Mathematica

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A035932 Smallest number that takes n steps to reach 0 under "k->max product of 2 numbers whose concatenation is k".

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A035933 Smallest number that takes n steps to reach 0 under "k->min product of 2 numbers whose concatenation is k".

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