A137239 a(n) is the number of Catalan numbers with n digits.

4, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2

Offset

1,1

Comments

The sequence contains only one 4 and no 3's (the other terms being 1's and 2's). - Paolo Xausa, Sep 26 2025

Links

J. Mulder, Table of n, a(n) for n = 1..12034

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log_4 (10) = 1.660964... (A154155). - Amiram Eldar, Sep 26 2025

Example

1-digit Catalan numbers are 1, 1, 2, and 5 so a(1) = 4.
2-digits Catalan numbers are 14 and 24 so a(2) = 2.

Mathematica

Map[Length, Most[Split[IntegerLength[CatalanNumber[Range[0, 200]]]]]] (* Paolo Xausa, Sep 26 2025 *)

Crossrefs

Cf. A000108, A154155.

Run lengths of A389231.

Sequence in context: A282698 A136709 A254969 * A136714 A280135 A297825

Adjacent sequences: A137236 A137237 A137238 * A137240 A137241 A137242

Keyword

nonn,base,easy

Author

Ctibor O. Zizka, Mar 09 2008

Extensions

Corrected and extended by Sean A. Irvine, Feb 07 2010

Status

approved