OFFSET
1,1
COMMENTS
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).
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
EXAMPLE
a(1) = 497 because lcm(78-33, 33) = 497-2, lcm(78-7, 7) = 497.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jun 06 2005
EXTENSIONS
More terms from Robert G. Wilson v, Jun 11 2005
STATUS
approved