A242897 Catalan numbers C(n) such that sum of the factorials of digits of C(n) is semiprime.

14, 42, 132, 4862, 35357670, 1767263190, 91482563640, 4861946401452, 212336130412243110, 2622127042276492108820, 10113918591637898134020, 39044429911904443959240, 116157871455782434250553845880, 6852456927844873497549658464312, 368479169875816659479009042713546950

Offset

1,1

Comments

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.

Intersection of A000108 and A242868.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..347

Example

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.

Maple

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);

Mathematica

Select[CatalanNumber[Range[70]], PrimeOmega[Total[IntegerDigits[#]!]]==2&] (* Harvey P. Dale, Dec 13 2022 *)

Crossrefs

Cf. A000108, A001358, A061602, A242855, A242868.

Sequence in context: A244101 A212514 A292051 * A120714 A041378 A302219

Adjacent sequences: A242894 A242895 A242896 * A242898 A242899 A242900

Keyword

nonn,base,less

Author

K. D. Bajpai, May 25 2014

Status

approved