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A069638 "Sorted" sum of two previous terms, beginning with 0,1. "Sorted" means to sort the digits of the sum in ascending order.

%I A069638 #28 Aug 31 2022 16:00:49
%S A069638 0,1,1,2,3,5,8,13,12,25,37,26,36,26,26,25,15,4,19,23,24,47,17,46,36,
%T A069638 28,46,47,39,68,17,58,57,115,127,224,135,359,449,88,357,445,28,347,
%U A069638 357,47,44,19,36,55,19,47,66,113,179,229,48,277,235,125,36,116,125,124,249,337
%N A069638 "Sorted" sum of two previous terms, beginning with 0,1. "Sorted" means to sort the digits of the sum in ascending order.
%C A069638 The maximum value in this sequence is 667. After the 75th term, the next 120 terms (a(76) - a(195)) repeat as a group infinitely.
%H A069638 Zak Seidov, <a href="/A069638/b069638.txt">Table of n, a(n) for n = 0..1000</a>
%F A069638 a(n) = SORT[a(n-1) + a(n-2)].
%e A069638 a(8)=12 because a(7)+a(6)=13+8=21 and the digits of 21 sorted in ascending order = 12.
%e A069638 Also a(17)=4 because a(16)+a(15)=15+25=40 and the digits of 40 sorted in ascending order = 04, or just 4;
%p A069638 a:= proc(n) option remember; `if`(n<2, n, parse(cat(
%p A069638       sort(convert(a(n-1)+a(n-2), base, 10))[])))
%p A069638     end:
%p A069638 seq(a(n), n=0..77);  # _Alois P. Heinz_, Aug 31 2022
%t A069638 a[0]:=0
%t A069638 a[1]:=1
%t A069638 a[n_] := a[n]=FromDigits[Sort[IntegerDigits[a[n-1]+a[n-2]]]] (* _Peter J. C. Moses_, Feb 08 2014 *)
%t A069638 nxt[{a_,b_}]:={b,FromDigits[Sort[IntegerDigits[a+b]]]}; NestList[nxt,{0,1},70][[All,1]] (* _Harvey P. Dale_, Jul 27 2020 *)
%o A069638 (Python)
%o A069638 a, terms = [0, 1], 66
%o A069638 [a.append(int("".join(sorted(str(a[-2]+a[-1]))))) for n in range(2, terms)]
%o A069638 print(a) # _Michael S. Branicky_, Aug 31 2022
%Y A069638 Cf. A000045, A001129, A004185, A237575, A237671.
%K A069638 nonn,base
%O A069638 0,4
%A A069638 _Gil Broussard_, Jan 16 2004