This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108564 #14 Jan 17 2022 11:40:51
%S A108564 0,1,1,2,4,8,15,29,56,18,118,122,134,239,136,136,456,679,147,1148,234,
%T A108564 228,1577,1378,1347,345,4467,3577,3679,1268,11299,12389,23568,24458,
%U A108564 11477,12789,22279,137,24668,35789,23788,23488,13377,24469,12258,23579
%N A108564 a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 4, for n>3: a(n+1) = SORT[a(n) + a(n-1) + a(n-2) + a(n-3)], where SORT places digits in ascending order and deletes 0's.
%C A108564 Sorted tetranacci numbers, a.k.a. sorted Fibonacci 4-step sequence.
%C A108564 As found by _T. D. Noe_: Max=4556699. Cycle period=41652. Cycle starts with the 23944th term.
%H A108564 Harvey P. Dale, <a href="/A108564/b108564.txt">Table of n, a(n) for n = 0..1000</a>
%H A108564 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.
%e A108564 a(8) = SORT[a(4) + a(5) + a(6) + a(7)] = SORT[108] = 18.
%e A108564 a(10) = SORT[a(6) + a(7) + a(8) + a(9)] = SORT[221] = 122.
%t A108564 nxt[{a_,b_,c_,d_,e_}]:={b,c,d,e,FromDigits[Sort[DeleteCases[ IntegerDigits[ b+c+d+e],_?0]]]}; NestList[nxt,{0,1,1,2,4},50][[All,1]] (* _Harvey P. Dale_, Jan 17 2022 *)
%Y A108564 Cf. A000078, A069638, A107281, A108565-A108573.
%K A108564 base,easy,nonn
%O A108564 0,4
%A A108564 _Jonathan Vos Post_, Jun 10 2005