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A166227
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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(793312220) =388244100 and dsf(388244100) = 33554978,...,dsf(387467199) = 793312220,.. in this way this 40 numbers make a loop for the function dsf.
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793312220, 388244100, 33554978, 405027808, 34381363, 16824237, 17647707, 3341086, 16824184, 33601606, 140025, 3388, 33554486, 16830688, 50424989, 791621836, 405114593, 387427281, 35201810, 16780376, 18517643, 17650825
(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 793312220 we can get a loop of the length of 40.
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EXAMPLE
| This is an reiterative process that starts with 7793312220.
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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, 7793312220, 80]
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CROSSREFS
| A165942, A166024, A166072, A166121
Sequence in context: A058420 A166121 A046186 * A104829 A198173 A204499
Adjacent sequences: A166224 A166225 A166226 * A166228 A166229 A166230
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KEYWORD
| base,nonn
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AUTHOR
| Ryohei Miyadera, Takuma Nakaoka and Koichiro Nishimura. (Miyadera127(AT)aol.com), Oct 09 2009
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