|
%I #4 Jul 30 2015 22:25:35
%S 497,623,875,1017,1107,1199,1397,1617,1991,2093,2277,2737,2795,2873,
%T 3077,3215,3383,3629,3743,3885,4097,4427,5453,5733,6233,6275,6327,
%U 6443,7049,8381,8759,8903,9947,10013,10127,10991,11225,11397,11613,11687
%N Odd numbers n such that there exists a solution to lcm(s,z-s) = n, lcm(t,z-t) = n-2 and 0 < s+t < z < n.
%C The alternating group on n letters for n>=5 odd can be generated by a 3-cycle x and an (n-2)-cycle y such that xy is an n-cycle. These are called standard generators. If we only know the orders of y and xy (and not their cycle shape) then this sequence gives values of n for which we may be misled into thinking that x and y are standard generators just by looking at their orders (y can be a permutation of shape (z-t)*t and xy can be a permutation of shape (z-s)*s).
%C Odd numbers n such that there exists a solution to lcm(r+s,t) = n-2, lcm(s,r+t) = n, 0< r,s,t and r+s+t <= n. - _Robert G. Wilson v_, Jun 11 2005
%e a(1) = 497 because lcm(78-33, 33) = 497-2, lcm(78-7, 7) = 497.
%t f[s_, t_, z_] := If[z < LCM[s, z - s] + 2 == LCM[t, z - t], LCM[t, z - t], 0]; t = Table[ f[s, t, z], {z, 6, 1500, 2}, {s, 1, Floor[z/2], 2}, {t, 1, Floor[z/2], 2}]; Take[ Union[ Flatten[t]], {2, 45}] (* _Robert G. Wilson v_, Jun 11 2005 *)
%K nonn
%O 1,1
%A Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jun 06 2005
%E More terms from _Robert G. Wilson v_, Jun 11 2005
|
