A035934 -id:A035934 - cp's OEIS frontend

A035935 Smallest number that always takes at least n steps to reach 0 under "k -> any product of 2 numbers whose concatenation is k".

0, 1, 11, 26, 39, 77, 666

Offset: 0

Next term is at least 3*10^7. 666 may be the last term. - Naohiro Nomoto, Apr 07 2001

Checked up to 1.55*10^10. No other numbers apart 666 with minimal path of length 6. The largest number found with minimal path equal to 5 is 711111. - Giovanni Resta, Oct 03 2012

Cf. A035930-A035934.

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 *)

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

cp's OEIS Frontend

A035935 Smallest number that always takes at least n steps to reach 0 under "k -> any product of 2 numbers whose concatenation is k".

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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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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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