This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A242855 #16 Apr 30 2025 19:38:40 %S A242855 2,16796,263747951750360,1002242216651368, %T A242855 104088460289122304033498318812080, %U A242855 22033725021956517463358552614056949950,1000134600800354781929399250536541864362461089950800,216489185503133990863274261791925599831188392742851863147080 %N A242855 Catalan numbers C(n) such that sum of the factorials of digits of C(n) is prime. %C A242855 The n-th Catalan number C(n) = (2*n)!/(n!*(n+1)!). %C A242855 The next term, a(9), has 66 digits which is too large to display in data section. %C A242855 The 102nd term, a(102), having 992 digits, is the last term in b-file. %C A242855 a(103) has 1021 digits, hence not included in b-file. %C A242855 Intersection of A000108 and A165451. %H A242855 K. D. Bajpai, <a href="/A242855/b242855.txt">Table of n, a(n) for n = 1..102</a> %e A242855 16796 = (2*10)!/(10!*(10+1)!) is 10th Catalan number: 1!+6!+7!+9!+6! = 369361 which is prime. %e A242855 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 A242855 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); %t A242855 Select[CatalanNumber[Range[150]],PrimeQ[Total[IntegerDigits[#]!]]&] (* _Harvey P. Dale_, Apr 30 2025 *) %Y A242855 Cf. A000040, A000108, A061602, A165451. %K A242855 nonn,base %O A242855 1,1 %A A242855 _K. D. Bajpai_, May 24 2014