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A166024 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(421845123) = 16780890 and dsf(16780890) = 421845123, so these 2 numbers make a loop for the function dsf. 4
421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In fact there are only 8 loops among all the nonnegative integers for the "dsf" function that we defined.

Periodic with period 2.

LINKS

Table of n, a(n) for n=1..24.

Ryohei Miyadera, Curious Properties of an Iterative Process,Mathsource, Wolfram Library Archive

Index entries for linear recurrences with constant coefficients, signature (0, 1).

FORMULA

a(n+1) = dsf(a(n)).

MATHEMATICA

dsf[n_] := Block[{m = n, t}, t = IntegerDigits[m]; Sum[Max[1, t[[k]]]^t[[k]], {k, Length[t]}]]; NestList[dsf, 421845123, 4]

LinearRecurrence[{0, 1}, {421845123, 16780890}, 24] (* Ray Chandler, Aug 25 2015 *)

CROSSREFS

Cf. A165942, A045503.

Sequence in context: A323537 A186795 A234193 * A234396 A017408 A017528

Adjacent sequences:  A166021 A166022 A166023 * A166025 A166026 A166027

KEYWORD

nonn,base,easy

AUTHOR

Ryohei Miyadera, Satoshi Hashiba and Koichiro Nishimura, Oct 04 2009

EXTENSIONS

Comment and editing by Charles R Greathouse IV, Aug 02 2010

STATUS

approved

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Last modified July 15 20:00 EDT 2019. Contains 325056 sequences. (Running on oeis4.)