OFFSET
1,1
COMMENTS
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.
LINKS
Ryohei Miyadera, Curious Properties of an Iterative Process, Mathsource, Wolfram Library Archive.
FORMULA
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.
EXAMPLE
This is an iterative process that starts with 1583236420.
MATHEMATICA
dsf[n_] := Block[{m = n, t}, t = IntegerDigits[m]; Sum[Max[1, t[[k]]]^t[[k]], {k, Length[t]}]]; NestList[dsf, 1583236420, 194]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ryohei Miyadera, Oct 13 2009
STATUS
approved