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A217712 Number of primes occurring exactly once as numerators in sums generated from the set 1, 1/2, 1/3,..., 1/n. 5
0, 1, 3, 3, 11, 13, 27, 54, 106, 168, 378, 142, 733, 1597, 1283, 3418, 8204, 10112, 24644, 7829, 32866, 78136, 178741, 37002, 256392, 650596, 1402914, 286854, 2053463 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For information about how often the numerator of the generated sums is prime, see A075188 and A075189; for the largest generated prime, see A075226; for the smallest odd prime not generated, see A075227.

LINKS

Table of n, a(n) for n=1..29.

EXAMPLE

For n=3 there are the following fractions as sums of 1, 1/2 and 1/3:

{1/3, 1/2, 5/6, 1, 4/3, 3/2, 11/6}, three numerators are prime and they occur exactly once, therefore a(3) = A075188(3) = A075189(3) = #{3, 5, 11} = 3;

n=4: adding 1/4 to the previous fractions gives together: 1/4, 1/3, 1/2, 1/3+1/4=7/12, 1/2+1/4=3/4, 5/6, 1, 5/6+1/4=13/12, 1+1/4=5/4, 4/3, 3/2, 4/3+1/4=19/12, 3/2+1/4=7/4, 11/6 and 11/6+1/4=25/12:

A075188(4) = #{7/12, 3/4, 5/6, 13/12, 5/4, 3/2, 19/12, 7/4, 11/6} = 9,

A075189(4) = #{3, 5, 7, 11, 13, 19} = 6,

a(4) = #{11, 13, 19} = 3.

PROG

(Haskell)

import Data.Ratio ((%), numerator)

import Data.Set (Set, empty, fromList, toList, union, size)

import Data.Set (member, delete, insert)

a217712 n = a217712_list !! (n-1)

a217712_list = f 1 empty empty where

   f x s s1 = size s1' : f (x + 1) (s `union` fromList hs) s1' where

     s1' = g s1 $ filter ((== 1) . a010051') $ map numerator hs

     g v []                    = v

     g v (w:ws) | w `member` v = g (delete w v) ws

                | otherwise    = g (insert w v) ws

     hs = map (+ 1 % x) $ 0 : toList s

CROSSREFS

Cf. A010051.

Sequence in context: A136123 A045495 A045494 * A321678 A027416 A281905

Adjacent sequences:  A217709 A217710 A217711 * A217713 A217714 A217715

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 02 2013

STATUS

approved

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Last modified August 4 08:30 EDT 2021. Contains 346445 sequences. (Running on oeis4.)