A231885 Primes of the form Catalan(n) - 1.

13, 41, 131, 1429, 4861, 477638699, 4861946401451, 5632681584560312734993915705849145099, 16435314834665426797069144960762886143367590394939, 171069509209912116706646841207804116182333282333996796075729541331934805254423

Offset

1,1

Comments

The 22nd term a(22) in the sequence has 862 digits.

a(23) has 1134 digits; a(25) has 1413 digits; a(30) has 2046 digits; a(31) has 2348 digits (these are not included in b-file).

Links

K. D. Bajpai, Table of n, a(n) for n = 1..22

Example

a(2)= 41: n= 5: (2*n)!/(n!*(n + 1)!)-1= 41 which is prime.
a(4)= 1429: n= 8: (2*n)!/(n!*(n + 1)!)-1= 1429 which is prime.

Maple

KD:= proc() local a; a:= (2*n)!/(n!*(n + 1)!)-1;  if isprime(a) then return(a):  fi;  end:  seq(KD(), n=1..150);

Mathematica

Select[CatalanNumber[Range[200]]-1, PrimeQ] (* Harvey P. Dale, Dec 21 2019 *)

Crossrefs

Cf. A000108 (Catalan numbers).

Cf. A053427 (numbers n : Catalan(n)-1 is prime).

Cf. A053429 (numbers n such that Catalan(n)+1 is prime).

Cf. A230061 (primes of the form Catalan(n)+1).

Sequence in context: A141970 A305155 A355965 * A167240 A147247 A028468

Adjacent sequences: A231882 A231883 A231884 * A231886 A231887 A231888

Keyword

nonn

Author

K. D. Bajpai, Nov 21 2013

Status

approved