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

5,1

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).

Links

Table of n, a(n) for n=5..34.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A176266, A007605.

Sequence in context: A177819 A126456 A126157 * A105715 A111821 A275546

Adjacent sequences: A176264 A176265 A176266 * A176268 A176269 A176270

Keyword

nonn,base

Author

Michel Lagneau, Dec 07 2010

Status

approved