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Search: id:A134411
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| A134411 |
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a(n) is the smallest positive integer such that the numerator of (sum{k=1 to n} 1/a(k)) is prime (or 1), for all positive integers n. |
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+0
5
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| 1, 1, 1, 2, 3, 1, 3, 1, 1, 2, 6, 1, 1, 2, 4, 1, 1, 1, 3, 1, 1, 2, 3, 1, 2, 3, 2, 1, 4, 6, 1, 3, 1, 3, 2, 8, 3, 2, 3, 3, 1, 2, 6, 2, 1, 3, 3, 1, 5, 4, 3, 2, 1, 3, 1, 4, 2, 1, 3, 2, 1, 3, 1, 1, 3, 1, 1, 2, 6, 2, 4, 5, 3, 1, 3, 2, 1, 3, 3, 1, 3
(list; graph; listen)
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OFFSET
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1,4
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EXAMPLE
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The sum of the reciprocals of the first 9 terms is 1 + 1 + 1 + 1/2 + 1/3 + 1 + 1/3 + 1 + 1 = 43/6. (And the numerator, 43, is prime.) Adding the reciprocal of 1 to this gets 49/6 (in reduced form). But 49 is composite. However, adding the reciprocal of 2 to 43/6 gets 23/3 (when written in reduced form). 23 is a prime, so therefore a(10) = 2.
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MATHEMATICA
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a = {1}; s = 1; Do[i = 1; While[ ! PrimeQ[Numerator[s + 1/i]], i++ ]; s = s + 1/i; AppendTo[a, i], {80}]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 27 2007
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CROSSREFS
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Cf. A134412, A134413.
Sequence in context: A118846 A082503 A064442 this_sequence A126044 A114899 A023678
Adjacent sequences: A134408 A134409 A134410 this_sequence A134412 A134413 A134414
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Oct 24 2007
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 27 2007
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