OFFSET
1,3
COMMENTS
Every prime is generated eventually. For the largest generated prime, see A075226. For the smallest odd prime not generated, see A075227.
A217712(n) = number of primes occurring exactly once as numerators among the 2^n sums. - Reinhard Zumkeller, Jun 02 2013
EXAMPLE
a(3) = 3 because 3 sums yield distinct prime numerators: 1+1/2 = 3/2, 1/2+1/3 = 5/6 and 1+1/2+1/3 = 11/6.
MATHEMATICA
Needs["DiscreteMath`Combinatorica`"]; maxN=20; For[lst={}; prms={}; i=0; n=1, n<=maxN, n++, While[i<2^n-1, i++; s=NthSubset[i, Range[n]]; k=Numerator[Plus@@(1/s)]; If[PrimeQ[k], prms=Union[prms, {k}]]]; AppendTo[lst, Length[prms]]]; lst
PROG
(Haskell)
import Data.Ratio ((%), numerator)
import Data.Set (Set, empty, fromList, toList, union, size)
a075189 n = a075189_list !! (n-1)
a075189_list = f 1 empty empty where
f x s s1 = size s1' : f (x + 1) (s `union` fromList hs) s1' where
s1' = s1 `union` fromList
(filter ((== 1) . a010051') $ map numerator hs)
hs = map (+ 1 % x) $ 0 : toList s
-- Reinhard Zumkeller, May 28 2013
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
T. D. Noe, Sep 08 2002
EXTENSIONS
Terms a(21)-a(29) by Reinhard Zumkeller, May 28 2013
STATUS
approved