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Search: id:A161664
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| 0, 0, 1, 2, 5, 7, 12, 16, 22, 28, 37, 43, 54, 64, 75, 86, 101, 113, 130, 144, 161, 179, 200, 216, 238, 260, 283, 305, 332, 354, 383, 409, 438, 468, 499, 526, 561, 595, 630, 662, 701, 735, 776, 814, 853, 895, 940, 978, 1024, 1068, 1115, 1161, 1212, 1258, 1309
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The original definition was: Safe periods for the emergence of cicada species on prime number cycles.
See Table 9 in reference, page 75, which together with the chart on page 73 (see link) provide a mathematical basis for the emergence of cicada species on prime number cycles.
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REFERENCES
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E. Haga, Eratosthenes goes bugs! Exploring Prime Numbers, 2007, pp 71-80; first publication 1994.
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LINKS
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E. Haga, Prime Safe Periods
A. Baker, Are there Genuine Mathematical Explanations of Physical Phenomena?, Mind 114 (454) (2005) 223-238.
G. F. Webb, The prime number periodical Cicada problem, Discr. Cont. Dyn. Syst. 1 (3) (2001) 387
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FORMULA
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a(n) = A000217(n)-A006218(n).
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EXAMPLE
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a(8) in A000217 minus a(8) in A006218 = a(7) above (28-16=12).
Referring to the chart referenced, when nth year = 7 there are 16 x-markers.
These represent unsafe periods for cicada emergence: 28-16=12 safe periods.
The percent of safe periods for the entire 7 years is 12/28=~42.86%; for year 7 alone the calculation is 5/7 = 71.43%, a relatively good time to emerge.
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CROSSREFS
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A000217, A049820, A006218.
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KEYWORD
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easy,nonn
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AUTHOR
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Enoch Haga (Enokh(AT)comcast.net), Jun 15 2009
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EXTENSIONS
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Simplified definition, offset corrected and partially edited by Omar E. Pol (info(AT)polprimos.com), Jun 18 2009
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