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A075189
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Number of unique primes in the numerator of the 2^n sums generated from the set 1, 1/2, 1/3,..., 1/n.
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3
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0, 1, 3, 6, 14, 20, 38, 74, 134, 232, 486, 526, 1078, 2036, 2505, 4762, 9929, 14598, 29831, 31521
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Every prime is generated eventually. 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 unique 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[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
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CROSSREFS
| Cf. A001008, A075135, A075188, A075226, A075227.
Sequence in context: A096337 A175318 A109757 * A200823 A093866 A056596
Adjacent sequences: A075186 A075187 A075188 * A075190 A075191 A075192
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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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