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Search: id:A114829
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| A114829 |
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Each term is previous term plus floor of geometric mean of all previous terms. |
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+0
1
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| 1, 2, 3, 4, 6, 8, 11, 14, 18, 23, 29, 36, 44, 53, 63, 74, 87, 101, 117, 135, 155, 177, 201, 227, 256
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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What is this sequence, asymptotically? a(n) is prime for n = 2, 3, 7, 10, 11, 14, 18, 24, ... are there an infinite number of prime values?
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LINKS
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Eric Weisstein's World of Mathematics, Geometric Mean.
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FORMULA
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a(1) = 1, a(n+1) = a(n) + floor(GeometricMean[a(1),a(2),...,a(n)]). a(n+1) = a(n) + [((a(1)*a(2)*,...,*a(n))^(1/n)].
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EXAMPLE
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a(2) = 1 + floor(1^(1/1)) = 1 + 1 = 2.
a(3) = 2 + floor[(1*2)^(1/2)] = 2 + floor[sqrt(2)] = 2 + 1 = 3.
a(4) = 3 + floor[(1*2*3)^(1/3)] = 3 + floor[CubeRoot(6)] = 3 + 1 = 4.
a(5) = 4 + floor[(1*2*3*4)^(1/4)] = 4 + floor[4thRoot(24)] = 4 + 2 = 6.
a(6) = 6 + floor[(1*2*3*4*6)^(1/5)] = 6 + floor[5thRoot(144)] = 6 + 2 = 8.
a(7) = 8 + floor[(1*2*3*4*6*8)^(1/6)] = 6 + floor[6thRoot(1152)] = 8 + 3 = 11.
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CROSSREFS
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Cf. A065094, A065095.
Sequence in context: A059291 A075535 A134953 this_sequence A007279 A034891 A143611
Adjacent sequences: A114826 A114827 A114828 this_sequence A114830 A114831 A114832
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 19 2006
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