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 A165942 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)). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Period 3. In fact there are only 8 such loops among all the nonnegative integers for the "dsf" function that we defined. LINKS Ryohei Miyadera, Curious Properties of an Iterative Process, Mathsource, Wolfram Library Archive Index entries for linear recurrences with constant coefficients, signature (0, 0, 1). 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. MATHEMATICA 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 *) CROSSREFS dsf is A045503. Sequence in context: A151772 A109482 A027886 * A179427 A031787 A228674 Adjacent sequences:  A165939 A165940 A165941 * A165943 A165944 A165945 KEYWORD nonn,base,easy AUTHOR Ryohei Miyadera, Daisuke Minematsu and Taishi Inoue, Oct 01 2009 EXTENSIONS Cross-reference from Charles R Greathouse IV, Nov 01 2009 Edited by Charles R Greathouse IV, Mar 18 2010 Extended by Ray Chandler, Aug 25 2015 STATUS approved

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Last modified October 23 22:13 EDT 2019. Contains 328373 sequences. (Running on oeis4.)