A240435 Catalan numbers whose sum of digits is a prime.

2, 5, 14, 16796, 208012, 18367353072152, 14544636039226909, 3116285494907301262, 45950804324621742364, 176733862787006701400, 270557451039395118028642463289168566420671280440, 3935312233584004685417853572763349509774031680023800

Offset: 1

Author

K. D. Bajpai, Apr 05 2014

Keywords

• nonn
• less
• base

Comments

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

The 40th term in the sequence, a(40), has 651 digits.

a(41), a(42), and a(43), which are not included in the b-file, have 1313, 1313, and 1317 digits, respectively.

Examples

			16796 is in sequence because Catalan(10) = (2*10)!/(10!*(10+1)!) = 16796: The digital sum(16796) = 29 which is prime.
208012 is in sequence because Catalan(12) = (2*12)!/(12!*(12+1)!) = 208012: The digital sum(208012) = 13 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A000108, A230061, A231885.

Programs

Maple

KD := proc() local a, b; a:=(2*n)!/(n!*(n+1)!); b:=add( i,i = convert((a), base, 10))(a);  if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..200);

Mathematica

Select[CatalanNumber[Range[100]],PrimeQ[Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Jul 19 2019 *)