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Search: id:A141214
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| A141214 |
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Defining A to be the interior angle of a regular polygon, the number of constructible regular polygons such that A is in a field extension <= degree 2^n, starting with n=0. This is also the number of values of x such that phi(x)/2 is a power of 2 <= 2^n (where phi is Euler's phi function), also starting with n=0. |
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+0
2
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| 3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250, 273, 297, 322, 348, 375, 403, 432, 462, 493, 525, 558, 592, 626, 660, 694
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OFFSET
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0,1
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FORMULA
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For 0<n<=31 (n+1)(n+6)/2 For n>=31 34n-462 The formulas are identical when n=31 f(31)=592
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EXAMPLE
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For degree 2^0, there are 3 polygons of sides 3, 4 & 6.
For degree 2^1, there are 4 polygons of sides 5, 8, 10 & 12.
For degree 2^2 there are 5 (15, 16, 20, 24 & 30).
For n<=31, for degree 2^n, there are n+3 polygons.
For n>= 31 there are 34 polygons.
Assuming there are only 5 Fermat primes, this is the value of the sum 3+4+5+... up to 31 (and 32) terms, after which each term is 34.
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CROSSREFS
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The first 32 terms are identical to A055998 and A027379.
Sequence in context: A072098 A140778 A095115 this_sequence A027379 A055998 A066379
Adjacent sequences: A141211 A141212 A141213 this_sequence A141215 A141216 A141217
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KEYWORD
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nonn
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AUTHOR
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Matthew Lehman (matt.comicopia(AT)gmail.com), Jun 14 2008
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