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Search: id:A166072
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| A166072 |
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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(809265896) =808491852 and dsf(808491852) = 437755524,...,dsf(792488396) = 809265896,.. in this way this 8 numbers make a loop for the function dsf. |
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4
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| 809265896, 808491852, 437755524, 1657004, 873583, 34381154, 16780909, 792488396, 809265896, 808491852, 437755524, 1657004, 873583, 34381154, 16780909, 792488396
(list; graph; listen)
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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. We have discovered this fact with the calculation by Mathematica and other general purpose languages.
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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 809265896 we can get a loop of the length of 8.
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EXAMPLE
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This is an reiterative process that starts with 809265896.
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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, 809265896, 16]
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CROSSREFS
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A165942, A166024
Sequence in context: A046186 A166227 A104829 this_sequence A152156 A017540 A132216
Adjacent sequences: A166069 A166070 A166071 this_sequence A166073 A166074 A166075
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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 06 2009
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