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A075226 Largest prime in the numerator of the 2^n sums generated from the set 1, 1/2, 1/3,..., 1/n. 6
3, 11, 19, 137, 137, 1019, 2143, 7129, 7129, 78167, 81401, 1085933, 1111673, 1165727, 2364487, 41325407, 41325407, 796326437, 809074601, 812400209, 822981689, 19174119571, 19652175721, 99554817251, 100483070801 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

For the smallest odd prime not generated, see A075227. For information about how often the numerator of these sums is prime, see A075188 and A075189. The Mathematica program also prints the subset that yields the largest prime. For n <=20, the largest prime occurs in a sum of n-2, n-1, or n reciprocals.

LINKS

Martin Fuller, Table of n, a(n) for n = 2..100

Martin Fuller, PARI program

EXAMPLE

a(3) =11 because 11 is largest prime numerator in the three sums that yield primes: 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[t={}; lst={}; mx=0; i=0; n=2, n<=maxN, n++, While[i<2^n-1, i++; s=NthSubset[i, Range[n]]; k=Numerator[Plus@@(1/s)]; If[PrimeQ[k], If[k>mx, t=s]; mx=Max[mx, k]]]; Print[n, " ", t]; AppendTo[lst, mx]]; lst

Table[Max[Select[Numerator[Total/@Subsets[1/Range[n], {2, 2^n}]], PrimeQ]], {n, 2, 30}] (* The program will take a long time to run. *) (* Harvey P. Dale, Jan 08 2019 *)

PROG

(Haskell)

import Data.Ratio (numerator)

a075226 n = a075226_list !! (n-1)

a075226_list = f 2 [recip 1] where

   f x hs = (maximum $ filter ((== 1) . a010051') (map numerator hs')) :

            f (x + 1) hs' where hs' = hs ++ map (+ recip x) hs

-- Reinhard Zumkeller, May 28 2013

(PARI) See Fuller link.

CROSSREFS

Cf. A001008, A075135, A075188, A075189, A075227, A010051, A217712.

Sequence in context: A128996 A196174 A192591 * A192598 A028978 A082628

Adjacent sequences:  A075223 A075224 A075225 * A075227 A075228 A075229

KEYWORD

nice,nonn

AUTHOR

T. D. Noe, Sep 08 2002

EXTENSIONS

More terms from Martin Fuller, Jan 19 2008

STATUS

approved

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Last modified November 13 08:18 EST 2019. Contains 329093 sequences. (Running on oeis4.)