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A076050 Limiting sequence if we start with 2 and successively replace n with 2,3,4,...,n,n+1. 5
2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

We get 2, 23, 23234, 23234232342345 and so on. The lengths are 1,2,5,14,42,... which are the Catalan numbers: A000108. The sums of the numbers in these strings are also the Catalan numbers.

In A071159 the n-digit terms follow the 2, 3, 2, 3, 4... rule: the number of terms in which the first n-1 digits are the same is 2, 3, 2, 3, 4, ... and the last digits of the terms are 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 4, ..., A007001. For example, 1111, 1112, 1121, 1122, 1123, 1211, 1212, 1221, 1222, 1223, 1231, 1232, 1233, 1234.

a(A000108(n)) = n+1 and a(m) < n+1 for m < A000108(n). [Reinhard Zumkeller, Feb 17 2012]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

PROG

(PARI) a(n)=local(v, w); if(n<1, 0, v=[1]; while(#v<n, w=[]; for(i=1, #v, w=concat(w, vector(v[i]+1, j, j))); v=w); 1+v[n])

(Haskell)

a076050 n = a076050_list !! (n-1)

a076050_list = 2 : f [2] where

   f xs = (drop (length xs) xs') ++ (f xs') where

     xs' = concatMap ((enumFromTo 2) . (+ 1)) xs

-- Reinhard Zumkeller, Feb 17 2012

CROSSREFS

Cf. A000108, A071159. a(n)=A007001(n)+1.

Sequence in context: A257396 A237582 A097352 * A130799 A243519 A278102

Adjacent sequences:  A076047 A076048 A076049 * A076051 A076052 A076053

KEYWORD

easy,nonn,nice

AUTHOR

Miklos Kristof, Oct 30 2002

STATUS

approved

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Last modified May 27 22:57 EDT 2017. Contains 287210 sequences.