A166072 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(809265896) = 808491852 and dsf(808491852) = 437755524,...,dsf(792488396) = 809265896, so these 8 numbers make a loop for the function dsf.

809265896, 808491852, 437755524, 1657004, 873583, 34381154, 16780909, 792488396, 809265896, 808491852, 437755524, 1657004, 873583, 34381154, 16780909, 792488396, 809265896, 808491852, 437755524, 1657004, 873583

Offset

1,1

Comments

In fact there are only 8 loops among all the nonnegative integers for the "dsf" function that we defined. We have discovered this fact through calculations using Mathematica and general-purpose languages.

Periodic with period 8.

Links

Table of n, a(n) for n=1..21.

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 (0,0,0,0,0,0,0,1).

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, 809265896, 16]
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1}, {809265896, 808491852, 437755524, 1657004, 873583, 34381154, 16780909, 792488396}, 24] (* Ray Chandler, Aug 25 2015 *)

Crossrefs

Cf. A165942, A166024.

Sequence in context: A104829 A198173 A204499 * A152156 A017540 A132216

Adjacent sequences: A166069 A166070 A166071 * A166073 A166074 A166075

Keyword

nonn,base,easy

Author

Ryohei Miyadera, Satoshi Hashiba and Koichiro Nishimura, Oct 06 2009

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

Extended by Ray Chandler, Aug 25 2015

Status

approved