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 A076476 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. 1
 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; text; internal format)
 OFFSET 1,4 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? LINKS 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. 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 CROSSREFS Cf. A076477. Sequence in context: A132890 A295295 A069290 * A243200 A016733 A060234 Adjacent sequences:  A076473 A076474 A076475 * A076477 A076478 A076479 KEYWORD nonn,frac AUTHOR T. D. Noe, Oct 14 2002 STATUS approved

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Last modified February 22 15:52 EST 2019. Contains 320399 sequences. (Running on oeis4.)