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A166383 Let 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. dsf(1583236420) =1682731 and dsf(1682731) = 18470991,...,dsf(388290999) = 1583236420,.. in this way this 97 numbers make a loop for the function dsf. In fact this is the longest loop for dsf function in the set of all nonnegative integers. 0
1583236420, 16827317, 18470991, 792441996, 1163132183, 16823961, 404291050, 387424134, 17601586, 17697199, 1163955211, 387473430, 18424896, 421022094, 387421016, 17647705, 2520668, 16873662, 17740759, 389894501, 808398820 (list; graph; refs; listen; history; text; internal format)



In fact there are only 8 loops in the whole nonnegative integers for the dsf-function that we defined. We have discovered this fact with the calculation by Mathematica and other general purpose languages. We have presented 6 loops to this On-Line Encyclopedia of Integer Sequences, and other two loops are in fact fixed points {1} and {3435}. It is easy to see that dsf(1) = 1 and dsf(3435) = 3^3+4^4+3^3+5^5=3435.


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

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


Let 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. By applying the function dsf to 1583236420 repeatedly we can get a loop of the length of 97.


This is an iterative process that starts with 1583236420.


dsf[n_] := Block[{m = n, t}, t = IntegerDigits[m]; Sum[Max[1, t[[k]]]^t[[k]], {k, Length[t]}]]; NestList[dsf, 1583236420, 194]


Cf. A165942, A166024, A166072, A166121, A166227

Sequence in context: A273815 A258885 A216905 * A227444 A329463 A246250

Adjacent sequences: A166380 A166381 A166382 * A166384 A166385 A166386




Ryohei Miyadera, Oct 13 2009



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Last modified November 28 10:39 EST 2022. Contains 358411 sequences. (Running on oeis4.)