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A107281 a(0) = 1, a(1) = 1, a(2) = 2 and for n >= 1: a(n+1) = SORT[a(n) + a(n-1) + a(n-2)] where SORT places digits in ascending order and deletes 0's.

%I A107281 #18 Jun 01 2018 01:56:18
%S A107281 1,1,2,4,7,13,24,44,18,68,13,99,18,13,13,44,7,46,79,123,248,45,146,
%T A107281 349,45,45,349,349,347,145,148,46,339,335,27,17,379,234,36,469,379,
%U A107281 488,1336,223,247,168,368,378,149,589,1116,1458,1336,139,2339,1348,2368,556,2247
%N A107281 a(0) = 1, a(1) = 1, a(2) = 2 and for n >= 1: a(n+1) = SORT[a(n) + a(n-1) + a(n-2)] where SORT places digits in ascending order and deletes 0's.
%C A107281 The maximum value is 56899, which first occurs at a(275). The maximum next occurs at a(977). _T. D. Noe_ verified that the terms around a(275) and a(977) are the same. Hence the period is 977 - 275 = 702. The actual period starts at a(24) with the interesting terms 349, 45, 45, 349, 349. For some different initial conditions, the period is different. The point of the SORT operation here is that it "mixes" the sequence and the questions are, considering cycles as orbits, all about ergodicity. To turn this into the sorted Fibonacci sequence (A069638), use a(0)=0, a(1)=1, a(2)=1. This is a "base" sequence, but has analogs in other bases; for instance, SORT(base 2)[n] means count the 1's in the binary, call that k and output 2^(k-1). How does this sequence depend on SORT(base M)[n] for various M? Are there any initial values such that the sequence us unbounded? If not, how does cycle length depend upon initial values?
%H A107281 Richard I. Hess, <a href="http://www.pme-math.org/journal/issues/PMEJ.Vol.10.No.9.pdf">Problem 920: sorted Fibonacci sequence</a>, Pi Mu Epsilon Journal, Vol. 10 (Fall 1998) No. 9, pp. 754-755.
%F A107281 a(0) = 1, a(1) = 1, a(2) = 2 and for n>1: a(n+1) = SORT[a(n) + a(n-1) + a(n-2)] where SORT places digits in ascending order and deletes 0.
%e A107281 a(8) = 18 because a(5) + a(6) + a(7) = 13 + 24 + 44 = 81 and SORT(81) = 18.
%t A107281 nxt[{a_,b_,c_}]:=Module[{d=FromDigits[Sort[IntegerDigits[a+b+c]]]}, {b,c,d}]; Transpose[NestList[nxt,{1,1,2},65]][[1]]  (* _Harvey P. Dale_, Feb 07 2011 *)
%Y A107281 Cf. A000073, A069638.
%K A107281 base,easy,nonn
%O A107281 0,3
%A A107281 _Jonathan Vos Post_, Jun 08 2005