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%I #15 Apr 06 2014 08:46:27
%S 0,11,44,55,77,868,69996,2683862,6783876,268969862,37889398873,
%T 477788989887774
%N Smallest palindrome which has multiplicative persistence n.
%C Probably finite.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>
%H <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%e 0 has persistence 0.
%e 11 -> 1 has persistence 1.
%e 44 -> 16 -> 6 has persistence 2.
%e 55 -> 25 -> 10 -> 0 has persistence 3.
%e 77 -> 49 -> 36 -> 18 -> 8 has persistence 4.
%e 868 -> 384 -> 96 -> 54 -> 20 -> 0 has persistence 5.
%t 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 *)
%Y Cf. A031346, A003001, A002113.
%K nonn,base,fini,nice
%O 0,2
%A _Arkadiusz Wesolowski_, Dec 07 2011
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