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A296023
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Numbers n such that there is precisely 1 group of order n and 2 of order n + 1.
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2
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3, 5, 13, 33, 37, 61, 73, 85, 133, 141, 145, 157, 177, 193, 213, 217, 277, 313, 345, 393, 397, 421, 445, 457, 481, 501, 537, 541, 553, 561, 565, 613, 661, 673, 697, 705, 717, 733, 745, 757, 793, 817, 865, 877, 885, 913, 933, 957, 973, 997, 1041, 1093, 1141, 1153
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OFFSET
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1,1
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COMMENTS
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Being a subsequence of A003277, all the terms are odd.
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LINKS
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FORMULA
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EXAMPLE
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3 is in the sequence because 3 is a cyclic number and A000001(4) = 2. 5 is in the sequence because 5 is a cyclic number and A000001(6) = 2. Although 7 is a cyclic number, 7 is not in the sequence because A000001(8) = 5.
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MAPLE
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with(GroupTheory): with(numtheory):
for n from 1 to 10^3 do if [NumGroups(n), NumGroups(n+1)]=[1, 2] then print(n); fi; od;
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PROG
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(GAP) A296023 := Filtered([1..2014], n -> [NumberSmallGroups(n), NumberSmallGroups(n+1)]=[1, 2]);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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