A242855 Catalan numbers C(n) such that sum of the factorials of digits of C(n) is prime.

2, 16796, 263747951750360, 1002242216651368, 104088460289122304033498318812080, 22033725021956517463358552614056949950, 1000134600800354781929399250536541864362461089950800, 216489185503133990863274261791925599831188392742851863147080

Offset: 1

Author

K. D. Bajpai, May 24 2014

Keywords

• nonn
• base

Comments

The n-th Catalan number C(n) = (2*n)!/(n!*(n+1)!).

The next term, a(9), has 66 digits which is too large to display in data section.

The 102nd term, a(102), having 992 digits, is the last term in b-file.

a(103) has 1021 digits, hence not included in b-file.

Intersection of A000108 and A165451.

Examples

			16796 = (2*10)!/(10!*(10+1)!) is 10th Catalan number: 1!+6!+7!+9!+6! = 369361 which is prime.
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.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..102

Crossrefs

Cf. A000040, A000108, A061602, A165451.

Programs

Maple

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);

Mathematica

Select[CatalanNumber[Range[150]],PrimeQ[Total[IntegerDigits[#]!]]&] (* Harvey P. Dale, Apr 30 2025 *)