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A176267 a(n) = binomial(prime(n),s)/prime(n) where s is the sum of the decimal digits of prime(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 12 21:10 EDT 2020. Contains 336440 sequences. (Running on oeis4.)