OFFSET
1,1
COMMENTS
Period 3. In fact there are only 8 such loops among all the nonnegative integers for the "dsf" function that we defined.
LINKS
Ryohei Miyadera, Curious Properties of an Iterative Process, Mathsource, Wolfram Library Archive.
Shoei Takahashi, Unchone Lee, Hikaru Manabe, Aoi Murakami, Daisuke Minematsu, Kou Omori, and Ryohei Miyadera, Curious Properties of Iterative Sequences, arXiv:2308.06691 [math.GM], 2023.
Index entries for linear recurrences with constant coefficients, signature (0,0,1).
EXAMPLE
a(2) = dsf(a(1)) = dsf(3418) = 3^3+4^4+1^1+8^8 = 16777500; a(3) = dsf(16777500) = 1^1+6^6+7^7+7^7+7^7+5^5+0^0+0^0 = 2520413; a(4) = dsf(2520413) = 2^2+5^5+2^2+0^0+4^4+1^1+3^3 = 3418.
This is an iterative process that starts with 3418.
MATHEMATICA
dsf[n_] := Block[{m = n, t}, t = IntegerDigits[m]; Sum[Max[1, t[[k]]]^t[[k]], {k, Length[t]}]]; NestList[dsf, 3418, 6]
LinearRecurrence[{0, 0, 1}, {3418, 16777500, 2520413}, 30] (* Ray Chandler, Aug 25 2015 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Ryohei Miyadera, Daisuke Minematsu and Taishi Inoue, Oct 01 2009
EXTENSIONS
Cross-reference from Charles R Greathouse IV, Nov 01 2009
Edited by Charles R Greathouse IV, Mar 18 2010
Extended by Ray Chandler, Aug 25 2015
STATUS
approved