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A045544
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Odd values of n for which a regular n-gon can be constructed by compass and straightedge.
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19
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3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535, 65537, 196611, 327685, 983055, 1114129, 3342387, 5570645, 16711935, 16843009, 50529027, 84215045, 252645135, 286331153, 858993459, 1431655765, 4294967295
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OFFSET
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1,1
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COMMENTS
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If there are no more Fermat primes, then 4294967295 is the last term in the sequence.
From Daniel Forgues, Jun 17 2011: (Start)
The 31 = 2^5 - 1 terms of this sequence are the nonempty products of distinct Fermat primes. The 5 known Fermat primes are in A019434.
Prepending the empty product, i.e., 1, to this sequence gives A004729.
The initial term for this sequence is thus a(1) (offset=1), since a(0) should correspond to the omitted empty product, term a(0) of A004729.
Rows 1 to 31 of Sierpiński's triangle, if interpreted as a binary number converted to decimal (A001317), give a(1) to a(31). (End)
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LINKS
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Table of n, a(n) for n=1..31.
Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m
OEIS Wiki, Constructible odd-sided polygons
OEIS Wiki, Sierpinski's triangle
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FORMULA
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Each term is the product of distinct odd Fermat primes.
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MATHEMATICA
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Union[Times@@@Rest[Subsets[{3, 5, 17, 257, 65537}]]] (* Harvey P. Dale, Sep 20 2011 *)
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CROSSREFS
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Cf. A019434. Essentially same as A004729.
Coincides with A001317 for the first 31 terms only. - Robert G. Wilson v, Dec 22 2001
Cf. A004729.
Sequence in context: A094358 A003527 A004729 * A001317 A053576 A197818
Adjacent sequences: A045541 A045542 A045543 * A045545 A045546 A045547
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KEYWORD
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hard,nonn,nice
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AUTHOR
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Ken Takusagawa
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STATUS
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approved
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