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A166072
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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(809265896) = 808491852 and dsf(808491852) = 437755524,...,dsf(792488396) = 809265896, so these 8 numbers make a loop for the function dsf.
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3
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809265896, 808491852, 437755524, 1657004, 873583, 34381154, 16780909, 792488396, 809265896, 808491852, 437755524, 1657004, 873583, 34381154, 16780909, 792488396
(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. We have discovered this fact with the calculation by Mathematica and other general purpose languages.
Periodic with period 8.
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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, 809265896, 16]
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CROSSREFS
| A165942, A166024
Sequence in context: A104829 A198173 A204499 * A152156 A017540 A132216
Adjacent sequences: A166069 A166070 A166071 * A166073 A166074 A166075
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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 06 2009
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EXTENSIONS
| Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Aug 02 2010
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