login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A242897 Catalan numbers C(n) such that sum of the factorials of digits of C(n) is semiprime. 1
14, 42, 132, 4862, 35357670, 1767263190, 91482563640, 4861946401452, 212336130412243110, 2622127042276492108820, 10113918591637898134020, 39044429911904443959240, 116157871455782434250553845880, 6852456927844873497549658464312, 368479169875816659479009042713546950 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A244101 A212514 A292051 * A120714 A041378 A302219
KEYWORD
nonn,base,less
AUTHOR
K. D. Bajpai, May 25 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)