A173868 Smallest prime > n-th Catalan number.

2, 3, 7, 17, 43, 137, 431, 1433, 4871, 16811, 58787, 208037, 742909, 2674453, 9694849, 35357711, 129644831, 477638741, 1767263209, 6564120463, 24466267027, 91482563651, 343059613667, 1289904147349, 4861946401453, 18367353072191, 69533550916031, 263747951750399

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Formula

From Amiram Eldar, Sep 24 2025: (Start)

a(n) = prime(A273974(n)+1) for n >= 4.

a(n) = A151800(A000108(n)).

a(n) = A151800(A173867(n)) for n >= 4. (End)

Mathematica

PrimeNext[n_]:=Module[{k=n+1}, While[ !PrimeQ[k], k++ ]; k]; f[n_]:=(2n)!/n!/(n+1)!; Table[PrimeNext[f[n]], {n, 40}]
a[n_] := NextPrime[CatalanNumber[n]]; Array[a, 26] (* Amiram Eldar, Sep 24 2025 *)

Crossrefs

Cf. A000108, A151800, A173867, A273974.

Sequence in context: A257553 A143013 A113483 * A274291 A358456 A208987

Adjacent sequences: A173865 A173866 A173867 * A173869 A173870 A173871

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 28 2010

Extensions

Name edited and more terms added by Amiram Eldar, Sep 24 2025

Status

approved