A165942 For a nonnegative integer n, define dsf(n) = n_1^{n_1}+n_2^{n_2}+n_3^{n_3} + n_m^{n_m}, where {n_1,n_2,n_3,...n_m} lists digits of n. Then starting with a(1) = 3418, a(n+1) = dsf(a(n)).

3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413

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

Table of n, a(n) for n=1..30.

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

dsf is A045503.

Sequence in context: A151772 A109482 A027886 * A179427 A031787 A228674

Adjacent sequences: A165939 A165940 A165941 * A165943 A165944 A165945

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