OFFSET
5,1
COMMENTS
Note that a(n) is always an integer, as binomial(p,s) = p! / ((p-s)!/s!) is always divisible by p for prime p because neither (p-s)! nor s! can contain a factor of p when 0 < s < p, which occurs when n >= 5. By contrast, for n < 5, p(n) < 10, the sum of digits is p(n) itself, and the result is 1/p(n).
EXAMPLE
For n = 6, prime(6) = 13, s = 1+3 = 4 and binomial(13, 4)/13 = 715/13 = 55.
MAPLE
MATHEMATICA
pn[n_]:=Module[{pr=Prime[n]}, Binomial[pr, Total[IntegerDigits[pr]]]/pr]; Array[pn, 40, 5] (* Harvey P. Dale, Mar 29 2012 *)
PROG
(Sage) A176267 = lambda n: binomial(nth_prime(n), sum(nth_prime(n).digits()))/nth_prime(n) # D. S. McNeil, Dec 08 2010
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Dec 07 2010
STATUS
approved