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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} lists digits of n. Then starting with a(1) = 3418, a(n+1) = dsf(a(n)).
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5
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3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413
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OFFSET
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1,1
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COMMENTS
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Period 3. In fact there are only 8 such loops among all the nonnegative integers for the "dsf" function that we defined.
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LINKS
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EXAMPLE
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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
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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]
LinearRecurrence[{0, 0, 1}, {3418, 16777500, 2520413}, 30] (* Ray Chandler, Aug 25 2015 *)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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