Search: id:A161664
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%I A161664
%S A161664 0,0,1,2,5,7,12,16,22,28,37,43,54,64,75,86,101,113,130,144,161,179,200,
%T A161664 216,238,260,283,305,332,354,383,409,438,468,499,526,561,595,630,662,
%U A161664 701,735,776,814,853,895,940,978,1024,1068,1115,1161,1212,1258,1309
%N A161664 Partial sums of A049820.
%C A161664 The original definition was: Safe periods for the emergence of cicada
species on prime number cycles.
%C A161664 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.
%D A161664 E. Haga, Eratosthenes goes bugs! Exploring Prime Numbers, 2007, pp 71-80;
first publication 1994.
%H A161664 E. Haga, Prime Safe Periods
%H A161664 A. Baker, Are there Genuine
Mathematical Explanations of Physical Phenomena?, Mind 114 (454)
(2005) 223-238.
%H A161664 G. F. Webb, The prime number periodical Cicada problem, Discr.
Cont. Dyn. Syst. 1 (3) (2001) 387
%F A161664 a(n) = A000217(n)-A006218(n).
%e A161664 a(8) in A000217 minus a(8) in A006218 = a(7) above (28-16=12).
%e A161664 Referring to the chart referenced, when nth year = 7 there are 16 x-markers.
%e A161664 These represent unsafe periods for cicada emergence: 28-16=12 safe periods.
%e A161664 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.
%Y A161664 A000217, A049820, A006218.
%Y A161664 Sequence in context: A080182 A001318 A024702 this_sequence A080547 A080555
A024924
%Y A161664 Adjacent sequences: A161661 A161662 A161663 this_sequence A161665 A161666
A161667
%K A161664 easy,nonn
%O A161664 1,4
%A A161664 Enoch Haga (Enokh(AT)comcast.net), Jun 15 2009
%E A161664 Simplified definition, offset corrected and partially edited by Omar
E. Pol (info(AT)polprimos.com), Jun 18 2009
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