|
Search: id:A161664
|
|
| |
|
| 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)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
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.
|
|
REFERENCES
|
E. Haga, Eratosthenes goes bugs! Exploring Prime Numbers, 2007, pp 71-80; first publication 1994.
|
|
LINKS
|
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
|
|
FORMULA
|
a(n) = A000217(n)-A006218(n).
|
|
EXAMPLE
|
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.
|
|
CROSSREFS
|
A000217, A049820, A006218.
Sequence in context: A080182 A001318 A024702 this_sequence A080547 A080555 A024924
Adjacent sequences: A161661 A161662 A161663 this_sequence A161665 A161666 A161667
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Enoch Haga (Enokh(AT)comcast.net), Jun 15 2009
|
|
EXTENSIONS
|
Simplified definition, offset corrected and partially edited by Omar E. Pol (info(AT)polprimos.com), Jun 18 2009
|
|
|
Search completed in 0.002 seconds
|
