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Search: id:A114831
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| A114831 |
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Each term is previous term plus floor of harmonic mean of two previous terms. |
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+0
1
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| 1, 2, 3, 5, 8, 11, 20, 34, 59, 102, 176, 305, 528, 914, 1583
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For two numbers x and y, HarmonicMean[x,y] = [(GeometricMean[x,y])^2] / Arithmetic Mean[x,y]. What is this sequence, asymptotically? a(n) is prime for n = 2, 3, 4, 6, 9, 15, ... are there an infinite number of prime values?
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LINKS
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Eric Weisstein's World of Mathematics, Harmonic Mean.
Eric Weisstein's World of Mathematics, Geometric Mean.
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FORMULA
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a(1) = 1, a(2) = 2, for n>2: a(n+1) = a(n) + floor(HarmonicMean[a(n),a(n-1)]). a(n+1) = a(n) + floor[(2*a(n)*a(n-1))/(a(n)+a(n-1))].
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EXAMPLE
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a(3) = 2 + floor[2*1*2/(1+2)] = 2 + floor[4/3] = 2 + 1 = 3.
a(4) = 3 + floor[2*2*3/(2+3)] = 3 + floor[12/5] = 3 + 2 = 5.
a(5) = 5 + floor[2*3*5/(3+5)] = 5 + floor[30/8] = 5 + 3 = 8.
a(6) = 8 + floor[2*5*8/(5+8)] = 5 + floor[80/13] = 5 + 6 = 11.
a(7) = 11 + floor[2*8*11/(8+11)] = 5 + floor[176/19] = 11 + 9 = 20.
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CROSSREFS
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Cf. A065094, A065095.
Sequence in context: A004693 A119014 A006258 this_sequence A092362 A105766 A056695
Adjacent sequences: A114828 A114829 A114830 this_sequence A114832 A114833 A114834
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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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