A166121 Let 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} is the list of the digits of an integer n. dsf(791621579) = 776537851 and dsf(776537851) = 19300779, ..., dsf(824599) = 791621579, ... in this way these 11 numbers make a loop for the function dsf.

791621579, 776537851, 19300779, 776488094, 422669176, 388384265, 50381743, 17604196, 388337603, 34424740, 824599, 791621579, 776537851, 19300779, 776488094, 422669176, 388384265, 50381743, 17604196, 388337603, 34424740

Offset

1,1

Comments

In fact there are only 8 loops among all the nonnegative integers for the "dsf" function that we defined. We have discovered this fact through calculations using Mathematica and general-purpose languages.

Links

Table of n, a(n) for n=1..21.

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.

Formula

Let 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} is the list of the digits of an integer n. By applying the function dsf to 791621579 we can get a loop of length 11.

Example

This is an reiterative process that starts with 791621579.

Mathematica

dsf[n_] := Block[{m = n, t}, t = IntegerDigits[m]; Sum[Max[1, t[[k]]]^t[[k]], {k, Length[t]}]]; NestList[dsf, 791621579, 22]

Crossrefs

Cf. A165942, A166024, A166072.

Sequence in context: A344729 A344730 A225389 * A348079 A046186 A166227

Adjacent sequences: A166118 A166119 A166120 * A166122 A166123 A166124

Keyword

base,nonn

Author

Ryohei Miyadera, Takuma Nakaoka and Koichiro Nishimura, Oct 07 2009

Status

approved