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

0,4

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A005150, A079668, A055186, A079686.

Sequence in context: A059959 A192812 A125127 * A114476 A260419 A117184

Adjacent sequences: A051117 A051118 A051119 * A051121 A051122 A051123

Keyword

nice,nonn,easy,base,look

Author

Jamie (sunshinebaby(AT)hotmail.com)

Extensions

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

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

Status

approved