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A166121
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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 this 11 numbers make a loop for the function dsf.
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791621579, 776537851, 19300779, 776488094, 422669176, 388384265, 50381743, 17604196, 388337603, 34424740, 824599, 791621579, 776537851, 19300779, 776488094, 422669176, 388384265, 50381743, 17604196, 388337603, 34424740
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| In fact there are only 8 loops in the whole nonnegative integers for the dsf-function that we defined. We have discovered this fact with the calculation by Mathematica and other general purpose languages.
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LINKS
| Ryohei Miyadera, Curious Properties of an Iterative Process,Mathsource, Wolfram Library Archive
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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 the length of 11.
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EXAMPLE
| This is an reiterative process that starts with 791621579.
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MATHEMATICA
| dsf[n_] := Block[{m = n, t}, t = IntegerDigits[m]; Sum[Max[1, t[[k]]]^t[[k]], {k, Length[t]}]]; NestList[dsf, 791621579, 22]
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CROSSREFS
| Cf. A165942, A166024, A166072
Sequence in context: A118876 A157788 A058420 * A046186 A166227 A104829
Adjacent sequences: A166118 A166119 A166120 * A166122 A166123 A166124
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KEYWORD
| base,nonn
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AUTHOR
| Ryohei Miyadera, Takuma Nakaoka and Koichiro Nishimura. (Miyadera127(AT)aol.com), Oct 07 2009
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