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%I #26 Apr 03 2023 10:36:13
%S 2,3,43,58787,4861946401453,337485502510215975556783793455058624701,
%T 4180080073556524734514695828170907458428751314321,
%U 1000134600800354781929399250536541864362461089950801,944973797977428207852605870454939596837230758234904051
%N Primes of the form Catalan(n)+1.
%C The 25th term a(25) in the sequence has 693 digits.
%C 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
%H K. D. Bajpai, <a href="/A230061/b230061.txt">Table of n, a(n) for n = 1..25</a>
%H Chris K. Caldwell and G. L. Honaker,Jr., <a href="https://t5k.org/curios/page.php?short=4250">Prime Curios! 4250</a>
%e a(3)= 43: Catalan(5)= (2*5)!/(5!*(5+1)!)= 42. Catalan(5)+1= 43 which is prime.
%e a(4)= 58787: Catalan(11)= (2*11)!/(11!*(11+1)!)= 58786. Catalan(11)+1= 58787 which is prime.
%p 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);
%t Select[CatalanNumber[Range[100]]+1,PrimeQ] (* _Harvey P. Dale_, Aug 26 2021 *)
%o (PARI) for(n=1,1e3,if(ispseudoprime(t=binomial(2*n,n)/(n+1)+1),print1(t", "))) \\ _Charles R Greathouse IV_, Oct 08 2013
%Y Cf. A000108, A024492, A141351.
%Y Cf. A053429 (numbers n such that Catalan(n)+1 is prime).
%K nonn
%O 1,1
%A _K. D. Bajpai_, Oct 08 2013
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