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The alternating group A_n contains an element x which is not conjugate to its inverse (equivalently not all the entries in the character table of A_n are real numbers).
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%I #6 Jun 20 2024 23:18:54

%S 3,4,7,8,9,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,

%T 31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,

%U 54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77

%N The alternating group A_n contains an element x which is not conjugate to its inverse (equivalently not all the entries in the character table of A_n are real numbers).

%C Every n >= 15 belongs to this sequence, i.e., the complement of this sequence is the finite sequence 1,2,5,6,10,14 for which all the entries in the character table of A_n are real.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%o (PARI) a(n)=if(n>8, n+6, [3, 4, 7, 8, 9, 11, 12, 13][n]) \\ _Charles R Greathouse IV_, Jun 20 2024

%K nonn,easy

%O 1,1

%A Ola Veshta (olaveshta(AT)my-deja.com), May 28 2001

%E More terms from _Sascha Kurz_, Mar 25 2002