A108157 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.

497, 623, 875, 1017, 1107, 1199, 1397, 1617, 1991, 2093, 2277, 2737, 2795, 2873, 3077, 3215, 3383, 3629, 3743, 3885, 4097, 4427, 5453, 5733, 6233, 6275, 6327, 6443, 7049, 8381, 8759, 8903, 9947, 10013, 10127, 10991, 11225, 11397, 11613, 11687

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

Links

Table of n, a(n) for n=1..40.

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

Sequence in context: A337952 A088845 A013685 * A062676 A097785 A145922

Adjacent sequences: A108154 A108155 A108156 * A108158 A108159 A108160

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