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
Offset: 1
Examples
dsf(421845123) = 16780890 and dsf(16780890) = 421845123, so these 2 numbers make a loop for the function dsf.
Links
- 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).
Programs
-
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 *)
Formula
a(n+1) = dsf(a(n)).
Extensions
Comment and editing by Charles R Greathouse IV, Aug 02 2010
Second sentence of Name moved to Example by Michael De Vlieger, Aug 24 2023
Comments