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A036059 The summarize Fibonacci sequence: summarize the previous two terms!.

%I A036059 #19 Jun 18 2022 13:24:01
%S A036059 1,1,21,1221,3231,233231,533221,15534221,3514334231,3534533241,
%T A036059 3544832231,183544733221,28172544634231,2827162554535241,
%U A036059 2827265554337241,2837267544338231,3847264544637221,3847362564636221,2837662564536221,2827863534537221,3837564524538221
%N A036059 The summarize Fibonacci sequence: summarize the previous two terms!.
%C A036059 After the 23rd term the sequence goes into a cycle of 16 terms.
%H A036059 Reinhard Zumkeller, <a href="/A036059/b036059.txt">Table of n, a(n) for n = 0..181</a>, 10 periods.
%H A036059 <a href="/index/Sa#swys">Index to sequences related to say what you see</a>
%e A036059 a(20) = 3837564524538221;
%e A036059 a(21) = 4837265534637221;
%e A036059 a(22+16*k) = 3837365544636221, k >= 0;
%e A036059 a(36) = a(20+16) = 3837265554834221 <> a(20);
%e A036059 a(37) = a(21+16) = 3837266544735221 <> a(21);
%e A036059 a(38) = a(22+16) = 3837365544636221 = a(22). - _Reinhard Zumkeller_, Aug 10 2014
%p A036059 a:= proc(n) option remember; `if`(n<2, 1, (p-> parse(cat(seq((c->
%p A036059      `if`(c=0, [][], [c, 9-i][]))(coeff(p, x, 9-i)), i=0..9))))(
%p A036059       add(x^i, i=map(x-> convert(x, base, 10)[], [a(n-1),a(n-2)]))))
%p A036059     end:
%p A036059 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jun 18 2022
%t A036059 a[0] = a[1] = 1; a[n_] := a[n] = FromDigits @ Flatten @ Reverse @ Select[ Transpose @ { DigitCount[a[n-1]] + DigitCount[a[n-2]], Append[ Range[9], 0]}, #[[1]] > 0&];
%t A036059 Table[a[n], {n, 0, 18}] (* _Jean-François Alcover_, Dec 30 2017 *)
%o A036059 (Haskell)
%o A036059 import Data.List (sort, group)
%o A036059 a036059 n = a036059_list !! n
%o A036059 a036059_list = map (read . concatMap show) fss :: [Integer] where
%o A036059    fss = [1] : [1] : zipWith h (tail fss) fss where
%o A036059          h vs ws = concatMap (\us -> [length us, head us]) $
%o A036059                    group $ reverse $ sort $ vs ++ ws
%o A036059 -- _Reinhard Zumkeller_, Aug 10 2014
%o A036059 (Python)
%o A036059 def aupton(nn):
%o A036059   alst = [1, 1]
%o A036059   for n in range(2, nn+1):
%o A036059     prev2, anstr = sorted(str(alst[-2]) + str(alst[-1])), ""
%o A036059     for d in sorted(set(prev2), reverse=True):
%o A036059       anstr += str(prev2.count(d)) + d
%o A036059     alst.append(int(anstr))
%o A036059   return alst
%o A036059 print(aupton(20)) # _Michael S. Branicky_, Feb 02 2021
%Y A036059 Cf. A036058, A036066.
%K A036059 nonn,base,nice,easy
%O A036059 0,3
%A A036059 _Floor van Lamoen_