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A242897
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Catalan numbers C(n) such that sum of the factorials of digits of C(n) is semiprime.
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1
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14, 42, 132, 4862, 35357670, 1767263190, 91482563640, 4861946401452, 212336130412243110, 2622127042276492108820, 10113918591637898134020, 39044429911904443959240, 116157871455782434250553845880, 6852456927844873497549658464312, 368479169875816659479009042713546950
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OFFSET
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1,1
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COMMENTS
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The n-th Catalan number is C(n) = (2*n)!/(n!*(n+1)!).
a(347), having 998 digits, is the last term in b-file.
a(348) has 1003 digits, hence is not included in b-file.
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LINKS
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EXAMPLE
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a(2) = 42 = (2*5)!/(5!*(5+1)!) is 5th Catalan number: 4!+2! = 26 = 2 * 13 which is semiprime.
a(4) = 4862 = (2*9)!/(9!*(9+1)!) is 9th Catalan number: 4!+8!+6!+2! = 41066 = 2 * 20533 which is semiprime.
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MAPLE
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with(numtheory): A242897:= proc() if bigomega(add( i!, i = convert(((2*n)!/(n!*(n+1)!)), base, 10))((2*n)!/(n!*(n+1)!)))=2 then RETURN ((2*n)!/(n!*(n+1)!)); fi; end: seq(A242897 (), n=1..100);
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MATHEMATICA
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Select[CatalanNumber[Range[70]], PrimeOmega[Total[IntegerDigits[#]!]]==2&] (* Harvey P. Dale, Dec 13 2022 *)
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CROSSREFS
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KEYWORD
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nonn,base,less
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AUTHOR
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STATUS
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approved
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