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%I #10 Jan 03 2016 15:32:48
%S 0,1,11,26,39,77,117,139,429,529,777,1117,1669,2238,2993,3697,4779,
%T 5319,5919,10998,11794,14989,21179,26869,27797,36177,38993,62958,
%U 74297,85797,95339,113319,125919,139919,199683,201799,247817,333329,360497,419926
%N Smallest number that can be made to take n steps to reach 0 under "k -> any product of 2 numbers whose concatenation is k".
%e a(6) = 117 since 117 -> 77 -> 49 -> 36 -> 18 -> 8 -> 0.
%t 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]
%Y Cf. A035930-A035935.
%K nonn,base,nice
%O 0,3
%A _Erich Friedman_
%E More terms from _Naohiro Nomoto_, Apr 11 2001
%E More terms from Vit Planocka (planocka(AT)mistral.cz), Feb 01 2003
%E More terms from _Martin Fuller_, Jun 02 2006
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