A201991 Smallest palindrome which has multiplicative persistence n.

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

Offset: 0

Author

Arkadiusz Wesolowski, Dec 07 2011

Keywords

• nonn
• base
• fini
• nice

Comments

Probably finite.

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Multiplicative Persistence
• Index entries for sequences related to palindromes

Crossrefs

Cf. A031346, A003001, A002113.

Programs

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 *)