A316563 Maximum order of an element in the special linear group SL(2, Z(n)).

1, 3, 6, 6, 10, 12, 14, 8, 18, 30, 22, 12, 26, 42, 30, 16, 34, 18, 38, 30, 42, 66, 46, 24, 50, 78, 54, 42, 58, 60, 62, 32, 66, 102, 70, 36, 74, 114, 78, 40, 82, 84, 86, 66, 90, 138, 94, 48, 98, 150, 102, 78, 106, 54, 110, 56, 114, 174, 118, 60, 122, 186, 126

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Prog

(GAP) Concatenation([1], List([2..15], n->Maximum(List(SL(2, Integers mod n), Order))));
(PARI)
MatOrder(M)={my(id=matid(#M), k=1, N=M); while(N<>id, k++; N=N*M); k}
a(n)={my(m=0); for(a=0, n-1, for(b=0, n-1, for(c=0, n-1, for(d=0, n-1, my(M=Mod([a, b; c, d], n)); if(matdet(M)==1, m=max(m, MatOrder(M))))))); m}

Crossrefs

Row lengths of A316564.

Cf. A000056, A316537, A316565.

Sequence in context: A184161 A276000 A333616 * A349212 A316140 A147849

Adjacent sequences: A316560 A316561 A316562 * A316564 A316565 A316566

Keyword

nonn

Author

Andrew Howroyd, Jul 06 2018

Status

approved