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 A108567 #16 May 09 2020 12:25:49
%S A108567 0,1,1,2,4,8,16,23,55,19,127,225,347,128,249,115,112,133,139,1223,299,
%T A108567 227,2248,1348,1567,157,679,2556,2788,11334,2249,1233,2699,23358,
%U A108567 12467,12568,5689,2366,368,15559,23577,24579,4678,16678,5788,12279,11338
%N A108567 a(0) = 0, a(1) = a(2) = 1, a(3) = 2, a(4) = 4, a(5) = 8, a(6) = 16, for n>5: a(n+1) = SORT[ a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6)], where SORT places digits in ascending order and deletes 0's.
%C A108567 _T. D. Noe_ found that the maximum is attained at a(4992871827) = 234444568999. The periodic part of this sequence begins at a(3544675600) and has length 5158842780.
%H A108567 Harvey P. Dale, <a href="/A108567/b108567.txt">Table of n, a(n) for n = 0..1000</a>
%H A108567 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 A108567 a(7) = SORT[a(0) + a(1) + a(2) + a(3) + a(4) + a(5) + a(6)] = SORT[0 + 1 + 1 + 2 + 4 + 8 + 16] = SORT[32] = 23.
%e A108567 a(8) = SORT[a(1) + a(2) + a(3) + a(4) + a(5) + a(6) + a(7)] = SORT[1 + 1 + 2 + 4 + 8 + 16 + 23] = SORT[55] = 55.
%e A108567 a(9) = SORT[a(2) + a(3) + a(4) + a(5) + a(6) + a(7) + a(8)] = SORT[1 + 2 + 4 + 8 + 16 + 23 + 55] = SORT[109] = 19.
%t A108567 nxt[{a_,b_,c_,d_,e_,f_,g_}]:={b,c,d,e,f,g,FromDigits[Sort[ IntegerDigits[ a+b+c+d+e+f+g]/.(0->Nothing)]]}; NestList[nxt,{0,1,1,2,4,8,16},50][[All,1]] (* _Harvey P. Dale_, May 09 2020 *)
%Y A108567 Cf. A066178, A069638, A107281, A108564-A108566, A108568-A108573.
%K A108567 base,easy,nonn
%O A108567 0,4
%A A108567 _Jonathan Vos Post_, Jun 11 2005