cp's OEIS Frontend

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)).

%I A166024 #21 Aug 24 2023 09:29:50
%S A166024 421845123,16780890,421845123,16780890,421845123,16780890,421845123,
%T A166024 16780890,421845123,16780890,421845123,16780890,421845123,16780890,
%U A166024 421845123,16780890,421845123,16780890,421845123,16780890,421845123,16780890,421845123,16780890
%N 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)).
%C A166024 In fact there are only 8 loops among all the nonnegative integers for the "dsf" function that we defined.
%C A166024 Periodic with period 2.
%H A166024 Ryohei Miyadera, <a href="http://library.wolfram.com/infocenter/MathSource/5686/">Curious Properties of an Iterative Process</a>, Mathsource, Wolfram Library Archive.
%H A166024 Shoei Takahashi, Unchone Lee, Hikaru Manabe, Aoi Murakami, Daisuke Minematsu, Kou Omori, and Ryohei Miyadera, <a href="https://arxiv.org/abs/2308.06691">Curious Properties of Iterative Sequences</a>, arXiv:2308.06691 [math.GM], 2023.
%H A166024 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A166024 a(n+1) = dsf(a(n)).
%e A166024 dsf(421845123) = 16780890 and dsf(16780890) = 421845123, so these 2 numbers make a loop for the function dsf.
%t A166024 dsf[n_] := Block[{m = n, t}, t = IntegerDigits[m]; Sum[Max[1, t[[k]]]^t[[k]], {k, Length[t]}]]; NestList[dsf, 421845123,4]
%t A166024 LinearRecurrence[{0, 1},{421845123, 16780890},24] (* _Ray Chandler_, Aug 25 2015 *)
%Y A166024 Cf. A165942, A045503.
%K A166024 nonn,base,easy
%O A166024 1,1
%A A166024 _Ryohei Miyadera_, Satoshi Hashiba and Koichiro Nishimura, Oct 04 2009
%E A166024 Comment and editing by _Charles R Greathouse IV_, Aug 02 2010
%E A166024 Second sentence of Name moved to Example by _Michael De Vlieger_, Aug 24 2023