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A166024
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Define dsf(n) = A045503(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 decimal digits of n. dsf(421845123) = 16780890 and dsf(16780890) = 421845123, so these 2 numbers make a loop for the function dsf.
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4
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421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890
(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.
Periodic with period 2.
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LINKS
| Ryohei Miyadera, Curious Properties of an Iterative Process,Mathsource, Wolfram Library Archive
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FORMULA
| a(n+1) = dsf(a(n)).
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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, 421845123, 4]
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CROSSREFS
| Cf. A165942, A045503
Sequence in context: A038132 A101770 A186795 * A017408 A017528 A117631
Adjacent sequences: A166021 A166022 A166023 * A166025 A166026 A166027
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KEYWORD
| nonn,base,easy
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AUTHOR
| Ryohei Miyadera, Satoshi Hashiba and Koichiro Nishimura. (Miyadera127(AT)aol.com), Oct 04 2009
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EXTENSIONS
| Comment and editing by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Aug 02 2010
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