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A075188
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Number of times that the numerator of a sum generated from the set 1, 1/2, 1/3,..., 1/n is prime.
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3
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0, 1, 3, 9, 19, 43, 79, 162, 307, 607, 1075, 2186, 3872, 7573, 15101, 29139, 52295, 104953, 189915, 379275
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Note that for each n there are only 2^(n-1) new sums to consider. Surprisingly, nearly half of the sums have a prime numerator. For the number of unique primes, see A075189. For the largest generated prime, see A075226. For the smallest odd prime not generated, see A075227.
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EXAMPLE
| a(3) = 3 because 3 sums yield prime numerators: 1+1/2 = 3/2, 1/2+1/3 = 5/6 and 1+1/2+1/3 = 11/6.
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MATHEMATICA
| Needs["DiscreteMath`Combinatorica`"]; maxN=20; For[cnt=0; lst={}; 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], cnt++ ]]; AppendTo[lst, cnt]]; lst
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CROSSREFS
| Cf. A001008, A075135, A075189, A075226, A075227.
Sequence in context: A145947 A153084 A147371 * A051894 A146393 A147431
Adjacent sequences: A075185 A075186 A075187 * A075189 A075190 A075191
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KEYWORD
| nice,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Sep 08 2002
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