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A166227
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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(793312220) = 388244100 and dsf(388244100) = 33554978, ..., dsf(387467199) = 793312220, ... in this way these 40 numbers make a loop for the function dsf.
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1
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793312220, 388244100, 33554978, 405027808, 34381363, 16824237, 17647707, 3341086, 16824184, 33601606, 140025, 3388, 33554486, 16830688, 50424989, 791621836, 405114593, 387427281, 35201810, 16780376, 18517643, 17650825, 17653671, 1743552, 830081, 33554462, 53476, 873607, 18470986, 421845378, 34381644, 16824695, 404294403, 387421546, 17651084, 17650799, 776537847, 20121452, 3396, 387467199, 793312220
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OFFSET
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1,1
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COMMENTS
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In fact there are only 8 loops among all the nonnegative integers for the "dsf" function that we defined. We have discovered this fact through calculations using Mathematica and general-purpose languages.
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LINKS
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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 793312220 we can get a loop of length 40.
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EXAMPLE
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This is an reiterative process that starts with 7793312220.
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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, 7793312220, 80]
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PROG
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(PARI) dsf(n) = my(d = digits(n)); sum(i=1, #d, d[i]^d[i]); \\ Michel Marcus, Apr 21 2014
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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