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

Author

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

Keywords

• base
• nonn

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.

Examples

			This is an reiterative process that starts with 791621579.
		

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.

Crossrefs

Cf. A165942, A166024, A166072.

Programs

Mathematica

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

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.