A176267 a(n) = binomial(prime(n),s)/prime(n) where s is the sum of the decimal digits of prime(n).

5, 55, 1430, 4862, 1463, 1193010, 1015, 9414328, 18278, 749398, 370577311, 16723070, 225398683020, 7151980, 378683037040, 149846840, 8511300512, 272994644359580, 194480021970, 8516063242041795, 8175951659117794, 50, 42925, 3046258475, 391139588190, 1242164, 1646644081775, 2271776, 38642514470976, 4683175503770976

Offset: 5

Author

Michel Lagneau, Dec 07 2010

Keywords

• nonn
• base

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).

Examples

			For n = 6, prime(6) = 13, s = 1+3 = 4 and binomial(13, 4)/13 = 715/13 = 55.
		

Crossrefs

Cf. A176266, A007605.

Programs

Maple

A007605 := proc(n) A007953(ithprime(n)) ; end proc:
A176267 := proc(n) local p; p := ithprime(n) ; binomial(p,A007605(n))/p ; end proc:
seq(A176267(n),n=5..20) ;

Mathematica

pn[n_]:=Module[{pr=Prime[n]},Binomial[pr,Total[IntegerDigits[pr]]]/pr]; Array[pn,40,5] (* Harvey P. Dale, Mar 29 2012 *)

Sage

A176267 = lambda n: binomial(nth_prime(n), sum(nth_prime(n).digits()))/nth_prime(n) # D. S. McNeil, Dec 08 2010