OFFSET
1,1
COMMENTS
The alternating groups A_n with n even can be generated by a 3-cycle x=(1,2,3) and an (n-1)-cycle y=(2,3,...n) whose product has cycle type 2 x (n-2). These are called standard generators of A_n. If we assume only that o(y)=n-1 and o(xy)=n-2, then for the values of n in the sequence, y could be the product of 2 cycles (cycle type (r+s).t) and xy can have cycle type s.(r+t). Thus the elements of the sequence give those alternating groups A_n which contain pairs of elements which look like standard generators if one only looks at their orders.
EXAMPLE
a(1)=58 because we can take r=11, s=8, t=3 giving lcm(19,3)=57, lcm(8,14)=56
MATHEMATICA
maxTerm = 3000; f[n_] := Module[{cond = False}, Do[r = rs-s; If[r == rt-t && r > 0 && r+s+t <= n, If[LCM[r+s, t] == n-1 && LCM[s, r+t] == n-2, cond = True; Break[]]], {t, Rest[Divisors[n-1]]}, {s, Divisors[n-2]}, {rs, Divisors[n-1]}, {rt, Divisors[n-2]}]; cond]; Reap[For[n = 0; k = 2, k <= maxTerm, k = k+2, If[f[k], n++; Print["a(", n, ") = ", k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, May 06 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jun 23 2005
STATUS
approved