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Search: id:A114830
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| A114830 |
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Each term is previous term plus ceiling of geometric mean of all previous terms. |
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+0
1
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| 1, 2, 4, 6, 9, 13, 18, 24, 31, 39, 48, 59, 71, 85, 101, 119, 139, 162, 187, 215, 246, 280, 318, 359, 404
(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, 6, 9, 12, 13, 15, 17, 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) + ceiling(GeometricMean[a(1),a(2),...,a(n)]). a(n+1) = a(n) + ceiling[((a(1)*a(2)*,...,*a(n))^(1/n)].
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EXAMPLE
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a(2) = 1 + ceiling(1^(1/1)) = 1 + 1 = 2.
a(3) = 2 + ceiling[(1*2)^(1/2)] = 2 + ceiling[sqrt(2)] = 2 + 2 = 4.
a(4) = 4 + ceiling[(1*2*4)^(1/3)] = 4 + ceiling[CubeRoot(8)] = 4 + 2 = 6.
a(5) = 6 + ceiling[(1*2*4*6)^(1/4)] = 6 + floor[4thRoot(48)] = 6 + 3 = 9.
a(6) = 9 + ceiling[(1*2*4*6*9)^(1/5)] = 9 + ceiling[5thRoot(432)] = 9 + 4 = 13.
a(7) = 13 + ceiling[(1*2*4*6*9*13)^(1/6)] = 6 + floor[6thRoot(5616)] = 13 + 5 = 18.
a(25) = 359 + ceiling[(1 * 2 * 4 * 6 * 9 * 13 * 18 * 24 * 31 * 39 * 48 * 59 * 71 * 85 * 101 * 119 * 139 * 162 * 187 * 215 * 246 * 280 * 318 * 359)^(1/24)] = 359 + ceiling[44.8074289] = 359 + 45 = 404.
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CROSSREFS
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Cf. A065094, A065095.
Adjacent sequences: A114827 A114828 A114829 this_sequence A114831 A114832 A114833
Sequence in context: A154255 A006697 A079717 this_sequence A001304 A000064 A001305
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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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