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

1, 1, 21, 1221, 3231, 233231, 533221, 15534221, 3514334231, 3534533241, 3544832231, 183544733221, 28172544634231, 2827162554535241, 2827265554337241, 2837267544338231, 3847264544637221, 3847362564636221, 2837662564536221, 2827863534537221, 3837564524538221

Offset

0,3

Comments

After the 23rd term the sequence goes into a cycle of 16 terms.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..181, 10 periods.

Index to sequences related to say what you see

Example

a(20) = 3837564524538221;
a(21) = 4837265534637221;
a(22+16*k) = 3837365544636221, k >= 0;
a(36) = a(20+16) = 3837265554834221 <> a(20);
a(37) = a(21+16) = 3837266544735221 <> a(21);
a(38) = a(22+16) = 3837365544636221 = a(22). - Reinhard Zumkeller, Aug 10 2014

Maple

a:= proc(n) option remember; `if`(n<2, 1, (p-> parse(cat(seq((c->
     `if`(c=0, [][], [c, 9-i][]))(coeff(p, x, 9-i)), i=0..9))))(
      add(x^i, i=map(x-> convert(x, base, 10)[], [a(n-1), a(n-2)]))))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 18 2022

Mathematica

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&];
Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Dec 30 2017 *)

Prog

(Haskell)
import Data.List (sort, group)
a036059 n = a036059_list !! n
a036059_list = map (read . concatMap show) fss :: [Integer] where
   fss = [1] : [1] : zipWith h (tail fss) fss where
         h vs ws = concatMap (\us -> [length us, head us]) $
                   group $ reverse $ sort $ vs ++ ws
-- Reinhard Zumkeller, Aug 10 2014
(Python)
def aupton(nn):
  alst = [1, 1]
  for n in range(2, nn+1):
    prev2, anstr = sorted(str(alst[-2]) + str(alst[-1])), ""
    for d in sorted(set(prev2), reverse=True):
      anstr += str(prev2.count(d)) + d
    alst.append(int(anstr))
  return alst
print(aupton(20)) # Michael S. Branicky, Feb 02 2021

Crossrefs

Cf. A036058, A036066.

Sequence in context: A086875 A012211 A297071 * A036519 A219408 A250061

Adjacent sequences: A036056 A036057 A036058 * A036060 A036061 A036062

Keyword

nonn,base,nice,easy

Author

Floor van Lamoen

Status

approved