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Search: id:A075226
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| A075226 |
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Largest prime in the numerator of the 2^n sums generated from the set 1, 1/2, 1/3,..., 1/n. |
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+0
4
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| 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; listen)
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OFFSET
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2,1
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COMMENT
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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.
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LINKS
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Martin Fuller, Table of n, a(n) for n = 2..100
Martin Fuller, PARI program
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EXAMPLE
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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.
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MATHEMATICA
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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
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CROSSREFS
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Cf. A001008, A075135, A075188, A075189, A075227.
Sequence in context: A048270 A088733 A128996 this_sequence A028978 A082628 A166096
Adjacent sequences: A075223 A075224 A075225 this_sequence A075227 A075228 A075229
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KEYWORD
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nice,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Sep 08 2002
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EXTENSIONS
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More terms from Martin Fuller (martin_n_fuller(AT)btinternet.com), Jan 19 2008
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