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A165942
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For a nonnegative integer n, define 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 a(n+1) = dsf(a(n)).
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5
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OFFSET
| 1,1
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COMMENTS
| Period 3. In fact there are only 8 such loops in the whole nonnegative integers for the dsf-function that we defined.
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LINKS
| Ryohei Miyadera, Curious Properties of an Iterative Process, Mathsource, Wolfram Library Archive
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EXAMPLE
| a(2) = dsf(a(1)) = dsf(3418) = 3^3+4^4+1^1+8^8 = 16777500; a(3) = dsf(16777500) = 1^1+6^6+7^7+7^7+7^7+5^5+0^0+0^0 = 2520413; a(4) = dsf(2520413) = 2^2+5^5+2^2+0^0+4^4+1^1+3^3 = 3418.
This is an iterative process that starts with 3418.
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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, 3418, 6]
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CROSSREFS
| dsf is A045503.
Sequence in context: A151772 A109482 A027886 * A179427 A031787 A024751
Adjacent sequences: A165939 A165940 A165941 * A165943 A165944 A165945
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KEYWORD
| nonn,base,easy
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AUTHOR
| Ryohei Miyadera, Daisuke Minematsu and Taishi Inoue (Miyadera127(AT)aol.com), Oct 01 2009
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EXTENSIONS
| Cross-reference from Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 01 2009
Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Mar 18 2010
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