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Search: id:A166024
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| A166024 |
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We define a function dsf. Let n be a non-negative integer, then 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(421845123) =16780890 and dsf(16780890) = 421845123, and in this way these 2 numbers make a loop for the function dsf. |
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5
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OFFSET
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1,1
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COMMENT
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In fact there are only 8 loops in the whole non-negative integers for the dsf-function that we defined.
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LINKS
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Ryohei Miyadera, Curious Properties of an Iterative Process,Mathsource, Wolfram Library Archive
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FORMULA
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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. By applying the function dsf to 421845123 we can get a loop of the length of 2.
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EXAMPLE
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This is an reiterative process that starts with 421845123.
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MATHEMATICA
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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
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A165942
Sequence in context: A103124 A038132 A101770 this_sequence A157729 A017408 A017528
Adjacent sequences: A166021 A166022 A166023 this_sequence A166025 A166026 A166027
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KEYWORD
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nonn
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AUTHOR
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Ryohei Miyadera, Satoshi Hashiba and Koichiro Nishimura. (Miyadera127(AT)aol.com), Oct 04 2009
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