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Search: id:A098294
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| A098294 |
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Smallest exponent of 2 which gives a power of 2 which is equal or bigger then (3/2)^n, n=0,1,... |
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+0
2
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| 0, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 40, 41, 41, 42, 43, 43, 44
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Stacking perfect fifths (the frequency ratio of a fifth is 3/2) this sequence determines into which octave the n-th fifth falls. For example, the third fifth, (3/2)^3, falls into the second octave, which means that it lies in the interval [2^1,2^2)=[2,4). The k-th octave comprises ratios in the interval [2^(k-1),2^k), k=1,2,...
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LINKS
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Pythagorean Scale.
Eric Weisstein's World of Music, Pythagorean Scale
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FORMULA
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2^a(n) >= (3/2)^n but 2^(a(n)-1)< (3/2)^n, n>=0.
a(n)= ceiling(tau*n) with tau:=ln(3)/ln(2)-1 =.584962501..., n>=0.
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EXAMPLE
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a(0)=0 because 2^0=1 = (3/2)^0 but 2^(-1)= 1/2 < 1. a(11)=7 because
2^7=128 > 86.497.. = (3/2)^11 but 2^6=64 < (3/2)^11.
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CROSSREFS
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Cf. A098295.
Sequence in context: A066683 A055038 A085268 this_sequence A077467 A005378 A103355
Adjacent sequences: A098291 A098292 A098293 this_sequence A098295 A098296 A098297
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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