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%I #14 May 25 2014 00:13:40
%S 2,16796,263747951750360,1002242216651368,
%T 104088460289122304033498318812080,
%U 22033725021956517463358552614056949950,1000134600800354781929399250536541864362461089950800,216489185503133990863274261791925599831188392742851863147080
%N Catalan numbers C(n) such that sum of the factorials of digits of C(n) is prime.
%C The n-th Catalan number C(n) = (2*n)!/(n!*(n+1)!).
%C The next term, a(9), has 66 digits which is too large to display in data section.
%C The 102nd term, a(102), having 992 digits, is the last term in b-file.
%C a(103) has 1021 digits, hence not included in b-file.
%C Intersection of A000108 and A165451.
%H K. D. Bajpai, <a href="/A242855/b242855.txt">Table of n, a(n) for n = 1..102</a>
%e 16796 = (2*10)!/(10!*(10+1)!) is 10th Catalan number: 1!+6!+7!+9!+6! = 369361 which is prime.
%e 263747951750360 = (2*28)!/(28!*(28+1)!) is 28th Catalan number: 2!+6!+3!+7!+4!+7!+9!+5!+1!+7!+5!+0!+3!+6!+0! = 379721 which is prime.
%p with(numtheory):A242855:= proc() if isprime(add( i!,i = convert(((2*n)!/(n!*(n+1)!)), base, 10))((2*n)!/(n!*(n+1)!))) then RETURN ((2*n)!/(n!*(n+1)!)); fi; end: seq(A242855 (), n=1..50);
%Y Cf. A000040, A000108, A061602, A165451.
%K nonn,base
%O 1,1
%A _K. D. Bajpai_, May 24 2014