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URL: https://oeis.org/A231885

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A231885
Primes of the form Catalan(k) - 1.
4
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
EXAMPLE
a(2) = 41: k = 5: (2*k)!/(k!*(k + 1)!)-1 = 41 which is prime.
a(4) = 1429: k = 8: (2*k)!/(k!*(k + 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 k : Catalan(k)-1 is prime).
Cf. A053429 (numbers k such that Catalan(k)+1 is prime).
Cf. A230061 (primes of the form Catalan(k)+1).
Sequence in context: A141970 A305155 A355965 * A167240 A147247 A028468
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Nov 21 2013
STATUS
approved