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Search: id:A165942
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| A165942 |
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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. Then dsf(3418) = 3^3+4^4+1^1+8^8 = 16777500, and dsf(16777500) = 1^1+6^6+7^7+7^7+7^7+5^5+0^0+0^0 = 2520413 and dsf(2520413) = 2^2+5^5+2^2+0^0+4^4+1^1+3^3 = 3418. In this way these three numbers make a loop. |
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+0
6
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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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EXAMPLE
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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(3418) = 16777500, dsf(16777500) = 2520413, and dsf(2520413) = 3418.
This is an iterative process that starts with 3418.
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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, 3418, 6]
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CROSSREFS
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dsf is A045503.
Sequence in context: A151772 A109482 A027886 this_sequence A031787 A024751 A024759
Adjacent sequences: A165939 A165940 A165941 this_sequence A165943 A165944 A165945
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KEYWORD
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nonn,base,new
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AUTHOR
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Ryohei Miyadera, Daisuke Minematsu and Taishi Inoue (Miyadera127(AT)aol.com), Oct 01 2009
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EXTENSIONS
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Cross-reference from Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 01 2009
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