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".

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

Author

Erich Friedman

Keywords

• nonn
• base
• nice

Examples

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

Crossrefs

Cf. A035930-A035935.

Programs

Mathematica

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]

Extensions

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