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Search: id:A117729
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| A117729 |
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Orders n of cyclic groups C_n such that the map "G -> Automorphism group of G" eventually reaches the trivial group when started at C_n. |
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+0
1
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| 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 14, 18, 19, 22, 23, 27, 38, 46, 47, 54, 81, 94, 162, 163, 243, 326, 486, 487, 729, 974, 1458, 1459, 2187, 2918, 4374, 6561, 13122, 19683, 39366, 39367, 59049, 78734, 118098, 177147, 354294, 531441, 1062882, 1594323, 3188646, 4782969
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If the map "G -> Automorphism group of G" eventually reaches the trivial group, then the initial group IS a cyclic group.
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FORMULA
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Consists of the following numbers:
3^i and 2*3^i for all i >= 0,
if 2*3^i+1 is a prime, then also 2*3^i+1 and 2(2*3^i+1),
the exceptional entries 4, 5, 10, 11, 22, 23, 46, 47 and 94.
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MAPLE
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t1:={ 4, 5, 10, 11, 22, 23, 46, 47, 94}; for i from 0 to 30 do t1:={op(t1), 3^i, 2*3^i}; if isprime(2*3^i+1) then t1:={op(t1), 2*3^i+1, 2*(2*3^i+1)}; fi; od: convert(t1, list); sort(%);
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CROSSREFS
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Sequence in context: A117730 A123101 A071557 this_sequence A073726 A008839 A039226
Adjacent sequences: A117726 A117727 A117728 this_sequence A117730 A117731 A117732
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KEYWORD
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nonn
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AUTHOR
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njas, based on communication from John Conway, Apr 14 2006
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