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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

Table of n, a(n) for n=1..30.

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.)