A165942 For a nonnegative integer n, define 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} lists digits of n. Then starting with a(1) = 3418, a(n+1) = dsf(a(n)).
3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413, 3418, 16777500, 2520413
Offset: 1
Examples
a(2) = dsf(a(1)) = dsf(3418) = 3^3+4^4+1^1+8^8 = 16777500; a(3) = dsf(16777500) = 1^1+6^6+7^7+7^7+7^7+5^5+0^0+0^0 = 2520413; a(4) = dsf(2520413) = 2^2+5^5+2^2+0^0+4^4+1^1+3^3 = 3418. This is an iterative process that starts with 3418.
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 (0,0,1).
Crossrefs
dsf is A045503.
Programs
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Mathematica
dsf[n_] := Block[{m = n, t}, t = IntegerDigits[m]; Sum[Max[1, t[[k]]]^t[[k]], {k, Length[t]}]]; NestList[dsf, 3418, 6] LinearRecurrence[{0, 0, 1},{3418, 16777500, 2520413},30] (* Ray Chandler, Aug 25 2015 *)
Extensions
Cross-reference from Charles R Greathouse IV, Nov 01 2009
Edited by Charles R Greathouse IV, Mar 18 2010
Extended by Ray Chandler, Aug 25 2015
Comments