A051120 Start with 1; at n-th step, write down what is in the sequence so far.

1, 1, 1, 3, 1, 1, 3, 4, 1, 1, 4, 2, 3, 6, 1, 1, 6, 2, 4, 3, 3, 1, 2, 8, 1, 1, 8, 2, 6, 3, 4, 5, 3, 3, 2, 11, 1, 1, 11, 2, 8, 3, 6, 1, 5, 4, 4, 8, 3, 5, 2, 13, 1, 1, 13, 2, 11, 4, 8, 4, 6, 3, 5, 6, 4, 10, 3, 7, 2, 16, 1, 1, 16, 2, 13, 3, 11, 1, 10, 5, 8, 1, 7, 6, 6, 4, 5, 9, 4, 12, 3, 9, 2, 18, 1

Offset: 0

Author

Jamie (sunshinebaby(AT)hotmail.com)

Keywords

• nice
• nonn
• easy
• base
• look

Examples

			After 1 1 1 3 1, we see "1 3 and 4 1's", so next terms are 1 3 4 1. Then "1 4, 2 3's, 6 1's"; etc.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005150, A079668, A055186, A079686.

Programs

Haskell

import Data.List (sort, nub, group)
a051120 n = a051120_list !! n
a051120_list = 1 : f [1] where
  f xs = seen ++ (f $ xs ++ seen) where
    seen = look (reverse $ map length $ group xs') (reverse $ nub xs')
    xs' = sort xs
    look [] []               = []
    look (cnt:cnts) (nr:nrs) = cnt : nr : look cnts nrs
-- Reinhard Zumkeller, Jun 22 2011

Mathematica

s={1}; Do[s=Flatten[{s,{Count[s,#],#}&/@Reverse[Union[s]]}], {60}]; s (* Peter J. C. Moses, Mar 21 2013 *)

Extensions

More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

a(28) corrected by Reinhard Zumkeller, Jun 22 2011