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Search: id:A121595
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| A121595 |
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Compressed version of A119788[n] (all entries equal to 1 are excluded). |
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+0
3
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| 5, 7, 5, 11, 13, 17, 7, 29, 7, 37, 19, 47, 119, 41, 23, 5, 29, 31, 11, 37, 37, 41, 43, 71, 13, 7, 13, 13, 47, 13, 49, 7, 7, 7, 53, 5, 79, 59, 97, 61, 71, 103, 67, 17, 71, 61, 73, 139, 17, 17, 79, 19, 19, 19, 83, 19, 151, 89, 29, 29, 263, 97
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also the ratio of numerators of n*H'[n]= A119787[n] and H'[n] = A058313[n] when they are different ( H'[n] is alternating harmonic number H'[n] = Sum[(-1)^(k+1)*1/k,{k,1,n}] ). The ratio of numerators A119787[n]/A058313[n] for n=1..400 is given in A119788[n]. It appears that most a(n) are prime divisors of corresponding indices A121594[n]. The first and only composite a(n) up to A119788[6000] is a(31) = 49 corresponding to A119788(1470). It appears that all a(n) belong to A092579[n] A sieve using the Fibonacci sequence over the integers >=2.
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FORMULA
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a(n) = A119788[A121594[n]], corresponding indices are given in A121594[n].
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MATHEMATICA
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Do[H=Sum[(-1)^(i+1)*1/i, {i, 1, n}]; a=Numerator[n*H]; b=Numerator[H]; If[ !Equal[a, b], Print[{n, a/b}]], {n, 1, 6000}]
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CROSSREFS
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Cf. A119788, A119787, A058313, A121594, A092579.
Sequence in context: A065746 A065478 A109353 this_sequence A125294 A139428 A063005
Adjacent sequences: A121592 A121593 A121594 this_sequence A121596 A121597 A121598
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 09 2006
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