A201991 Smallest palindrome which has multiplicative persistence n.

0, 11, 44, 55, 77, 868, 69996, 2683862, 6783876, 268969862, 37889398873, 477788989887774

Offset

0,2

Comments

Probably finite.

Links

Table of n, a(n) for n=0..11.

Eric Weisstein's World of Mathematics, Multiplicative Persistence

Index entries for sequences related to palindromes

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A031346, A003001, A002113.

Sequence in context: A259798 A239266 A259963 * A010819 A022703 A061976

Adjacent sequences: A201988 A201989 A201990 * A201992 A201993 A201994

Keyword

nonn,base,fini,nice

Author

Arkadiusz Wesolowski, Dec 07 2011

Status

approved