A176266 -id:A176266 - cp's OEIS frontend

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

Michel Lagneau, Dec 07 2010

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).

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

Cf. A176266, A007605.

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) ;

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

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica

Sage