0,2

Probably finite.

Eric Weisstein's World of Mathematics, Multiplicative Persistence

0 has persistence 0.

11 -> 1 has persistence 1.

44 -> 16 -> 6 has persistence 2.

55 -> 25 -> 10 -> 0 has persistence 3.

77 -> 49 -> 36 -> 18 -> 8 has persistence 4.

868 -> 384 -> 96 -> 54 -> 20 -> 0 has persistence 5.

lst = {}; int[n_] := IntegerDigits[n]; n = 0; Do[While[True, s = Length@int[n]; r = PadRight[int[n], 2*s, Reverse@int[n]]; If[s > 1, r = Drop[r, {s}]]; p = k = FromDigits[r]; c = 0; While[k > 9, k = Times @@ int[k]; c++]; If[c == l, Break[]]; n++]; AppendTo[lst, p], {l, 0, 10}]; lst (* Arkadiusz Wesolowski, Jul 05 2012 *)

Cf. A031346, A003001, A002113.

Sequence in context: A259798 A239266 A259963 * A010819 A022703 A061976

Adjacent sequences: A201988 A201989 A201990 * A201992 A201993 A201994

nonn,base,fini,nice

Arkadiusz Wesolowski, Dec 07 2011

approved