A166024 - OEIS

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. Starting with a(1) = 421845123, a(n+1) = dsf(a(n)).

421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890

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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.

Shoei Takahashi, Unchone Lee, Hikaru Manabe, Aoi Murakami, Daisuke Minematsu, Kou Omori, and Ryohei Miyadera, Curious Properties of Iterative Sequences, arXiv:2308.06691 [math.GM], 2023.

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

FORMULA

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

EXAMPLE

dsf(421845123) = 16780890 and dsf(16780890) = 421845123, so these 2 numbers make a loop for the function dsf.

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