A036106 A summarize Fibonacci sequence: summarize the previous two terms!.

1, 2, 1211, 2231, 133241, 14333231, 24632241, 1634534231, 261544434231, 262564533241, 363564435231, 464544634221, 463574533221, 17363574434221, 37263554634231, 37363554734231, 37364544933221, 1937263554933221

Offset: 0

Author

Floor van Lamoen

Keywords

• base
• easy
• nice
• nonn

Comments

From the 26th term the sequence gets into a cycle of 46.

Examples

			a(24) = 293847463554538221;
a(25) = 294827365564537221 = first term of first period;
a(26) = 293837366554537221;
a(70) = 294837364554538221 = last term of first period != a(24);
a(71) = 294827365564537221 = a(25) = first term of second period;
a(72) = 293837366554537221 = a(26);
a(116) = 294837364554538221 = a(70) = last term of second period;
a(117) = 294827365564537221 = a(71) = first term of third period.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..254 = 5 periods.
• Index to sequences related to say what you see

Crossrefs

Cf. A036059.

Programs

Haskell

import Data.List (sort, group); import Data.Function (on)
a036106 n = a036106_list !! n
a036106_list = 1 : 2 : map (read . concatMap say . reverse . group . sort)
               (zipWith ((++) `on` show) a036106_list $ tail a036106_list)
               where say ws = (show $ length ws) ++ [head ws]
-- Reinhard Zumkeller, Oct 05 2015

Mathematica

a[0] = 1; a[1] = 2; a[n_] := a[n] = Reverse /@ (IntegerDigits /@ {a[n-2], a[n-1]} // Flatten // Tally // Sort // Reverse) // Flatten // FromDigits; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Nov 02 2016 *)