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Search: id:A053194
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| A053194 |
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a(n) is the smallest number k such that cototient(k)=2n+1. |
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+0
1
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| 2, 9, 25, 15, 21, 35, 33, 39, 65, 51, 45, 95, 69, 63, 161, 87, 93, 75, 217, 99, 185, 123, 117, 215, 141, 235, 329, 159, 105, 371, 177, 135, 305, 427, 201, 335, 213, 207, 245, 511, 189, 395, 165, 415, 581, 267, 261, 623, 1501, 195, 485, 303, 225, 515, 321, 231
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OFFSET
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1,1
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COMMENT
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If the Goldbach conjecture holds, then for all odd numbers InvCot[2s-1] is non-empty.
All terms except a(1)=2 are odd numbers. All InvCototient[odd] sets seems to be non-empty, which does not hold for similar inverses of even numbers (see A005278).
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FORMULA
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a(n)=Min{x : A051953(x)=2n-1}.
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EXAMPLE
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n=17, a(n)=a(17)=75, EulerPhi(75)=40, cototient(75)=75-40=35=2*17+1=2n+1 n=11, a(11)=95 is the smallest in set {95,119,143,529,..} to the terms of which cototient[95]=cototient[119]=cototient[143]=cototient[529]= 95-72=119-96=143-120=529-506=23=2*11+1=2*n+1
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CROSSREFS
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Cf. A051953, A005278.
Sequence in context: A006973 A137852 A097346 this_sequence A005582 A116454 A124633
Adjacent sequences: A053191 A053192 A053193 this_sequence A053195 A053196 A053197
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Mar 02 2000
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