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A076476
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Fractions a(n)/n are such that gcd(a(n),n)=1, a(n) > 0 and a(n) is as small as possible so that the partial sums of the fractions have prime numerator. Let a(1)=1.
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1
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1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 5, 1, 1, 3, 1, 9, 1, 7, 4, 3, 1, 5, 1, 23, 9, 3, 10, 13, 13, 29, 7, 19, 5, 21, 2, 17, 2, 3, 7, 7, 5, 5, 6, 7, 1, 43, 3, 59, 27, 17, 4, 5, 9, 7, 1, 9, 2, 9, 7, 29, 8, 9, 4, 25, 3, 119, 2, 27, 4, 29, 4, 37, 5, 3, 2, 5, 9, 7, 10, 49, 1, 35, 12, 11, 6, 1, 22, 1, 13, 11, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| By Dirichlet's Theorem, it is always possible to find the next term. See A076477 for the list of primes appearing in the numerator. The denominators of these sums are the same as for harmonic numbers, A002805. The sum of the fractions diverges. Is there an upper bound for a(n)/n?
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EXAMPLE
| a(4) = 3 because 1/4 yields 1/1 + 1/2 + 1/3 + 1/4 = 25/12, but 3/4 yields 1/1 + 1/2 + 1/3 + 3/4 = 31/12.
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MATHEMATICA
| nMax = 100; lst = {1}; numer = {1}; s = 1; Do[k = 1; While[GCD[k, n] > 1 || ! PrimeQ[Numerator[s + k/n]], k++ ]; s = s + k/n; AppendTo[lst, k]; AppendTo[numer, Numerator[s]]; k++, {n, 2, nMax}]; lst
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CROSSREFS
| Cf. A076477.
Sequence in context: A191523 A132890 A069290 * A016733 A060234 A131270
Adjacent sequences: A076473 A076474 A076475 * A076477 A076478 A076479
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KEYWORD
| nonn,frac
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Oct 14 2002
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