A129631 Numbers k such that sum of digits of binomial(k+1, k-1) is a prime.

2, 6, 15, 20, 24, 31, 34, 43, 52, 61, 67, 70, 76, 85, 88, 91, 94, 97, 103, 106, 112, 115, 121, 124, 127, 130, 133, 136, 139, 141, 145, 151, 154, 160, 163, 166, 169, 178, 181, 190, 193, 196, 199, 200, 208, 211, 217, 226, 229, 232, 235, 238, 241, 247, 250, 259

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, May 31 2007

Keywords

• nonn
• base

Examples

			binomial(6+1,6-1)=binomial(7,5)=7!/(5!*2!)=21 --> 2+1=3 prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Maple

P:=proc(n) local i,k,w; for i from 1 by 1 to n do w:=0; k:=binomial(i+1,i-1); while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if isprime(w) then print(i); fi; od; end: P(1000);

Mathematica

Select[Range[300],PrimeQ[Total[IntegerDigits[Binomial[#+1,#-1]]]]&] (* Harvey P. Dale, Aug 13 2014 *)