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Search: id:A076474
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| A076474 |
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Denominators of the slowest decreasing sequence of unit fractions whose partial sums have a prime numerator. |
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3
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| 1, 2, 3, 5, 6, 10, 11, 13, 21, 23, 24, 29, 45, 48, 50, 51, 53, 54, 57, 58, 60, 68, 70, 81, 82, 98, 103, 104, 106, 120, 125, 128, 132, 139, 149, 164, 170, 192, 206, 214, 226, 228, 232, 235, 241, 257, 270, 275, 283, 305, 307, 314, 326, 351, 399, 412, 423, 436, 520
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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By Dirichlet's Theorem, it is always possible to find the next term. See A076475 for the list of primes appearing in the numerator. Does this sum of unit fractions converge?
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EXAMPLE
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For example, 1/1 + 1/2 = 3/2, 1/1 + 1/2 + 1/3 = 11/6. However, 1/4 is not in the sequence because 1/1 + 1/2 + 1/3 + 1/4 = 25/12 and 25 is not prime.
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MATHEMATICA
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nMax = 100; lst = {1}; numer = {1}; s = 1; i = 2; Do[While[ ! PrimeQ[Numerator[s + 1/i]], i++ ]; s = s + 1/i; AppendTo[lst, i]; AppendTo[numer, Numerator[s]]; i++, {n, 2, nMax}]; lst
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CROSSREFS
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Cf. A076475.
Cf. A127515, A134411.
Sequence in context: A047447 A094739 A063451 this_sequence A057760 A074243 A072720
Adjacent sequences: A076471 A076472 A076473 this_sequence A076475 A076476 A076477
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KEYWORD
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nonn,frac
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Oct 14 2002
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