OFFSET
1,1
COMMENTS
The 25th term a(25) in the sequence has 693 digits.
a(26) has 1335 digits; a(27) has 1647 digits; a(28) has 1694 digits; a(29) has 2554 digits; a(30) has 4857 digits; a(31) has 4876 digits; a(32) has 9641 digits. - Charles R Greathouse IV, Oct 09 2013
LINKS
K. D. Bajpai, Table of n, a(n) for n = 1..25
Chris K. Caldwell and G. L. Honaker,Jr., Prime Curios! 4250
EXAMPLE
a(3)= 43: Catalan(5)= (2*5)!/(5!*(5+1)!)= 42. Catalan(5)+1= 43 which is prime.
a(4)= 58787: Catalan(11)= (2*11)!/(11!*(11+1)!)= 58786. Catalan(11)+1= 58787 which is prime.
MAPLE
KD:= proc() local a, b, c; a:= (2*n)!/(n!*(n + 1)!); b:=a+1; if isprime(b) then return(b): fi; end: seq(KD(), n=1..50);
MATHEMATICA
Select[CatalanNumber[Range[100]]+1, PrimeQ] (* Harvey P. Dale, Aug 26 2021 *)
PROG
(PARI) for(n=1, 1e3, if(ispseudoprime(t=binomial(2*n, n)/(n+1)+1), print1(t", "))) \\ Charles R Greathouse IV, Oct 08 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Oct 08 2013
STATUS
approved