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A130742
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Reciprocal of the base 2 logarithm of the ratio between consecutive primes, rounded down.
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0
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1, 1, 2, 1, 4, 2, 6, 3, 2, 10, 3, 6, 14, 7, 5, 6, 20, 7, 11, 24, 8, 14, 9, 8, 17, 35, 18, 37, 19, 5, 22, 15, 47, 9, 51, 17, 18, 28, 19, 20, 62, 12, 66, 33, 68, 11, 12, 38, 79, 40, 27, 83, 17, 29, 30, 30, 93, 31, 48, 97, 19, 14, 53, 108, 54, 16, 38, 23, 120, 60, 41, 31, 42, 43, 66, 44, 34
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The power to which you must raise the fraction p(n+1)/p(n) to obtain a result which is greater than 2. It has been proved that lim inf of this sequence is (positive) infinity; eg. the ratio between subsequent primes tends to 1.
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FORMULA
| a(n) = floor(1 / log_2 (p(n) / p(n+1)))
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EXAMPLE
| a(5) = 4 because the sixth prime 11 divided by the fifth prime 13 has base two logarithm 0.241008.. and this lies between 1/4 and 1/5.
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MATHEMATICA
| f[n_] := Floor[1/Log[2, Prime[n + 1]/Prime[n]]]
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CROSSREFS
| Cf. A000523, A000040, A074461.
Sequence in context: A131888 A109170 A099311 * A130107 A107130 A194747
Adjacent sequences: A130739 A130740 A130741 * A130743 A130744 A130745
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KEYWORD
| easy,nonn
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AUTHOR
| Jack Grahl (j.grahl(AT)ucl.ac.uk), Jul 07 2007
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