The list of exact convering sequences with exactly one repeated  modulus (tha\

    t must be the largest) for up to, 32,  repeats

                    and where the largest modulus is <=, 500

[{}, {}, {}, {[3, [6, 4]]}, {}, {[3, [9, 6]], [4, [8, 6]], [3, 6, [12, 6]]}, {[
4, 6, [12, 7]], [3, 6, 9, [18, 7]]}, {[3, [12, 8]], [5, [10, 8]]}, {[4, [12, 9]
], [3, 6, [18, 9]], [4, 6, 8, 12, [24, 9]], [3, 6, 9, 12, 18, [36, 9]]}, {[3, [
15, 10]], [6, [12, 10]], [3, 9, [18, 10]], [4, 8, [16, 10]], [3, 6, 12, [24, 10
]]}, {[4, 6, 8, [24, 11]], [3, 6, 9, 12, [36, 11]]}, {[3, [18, 12]], [4, [16, 
12]], [5, [15, 12]], [7, [14, 12]], [3, 6, [24, 12]], [4, 6, 12, [24, 12]], [3,
6, 9, 18, [36, 12]]}, {[4, 10, [20, 13]], [6, 9, [18, 13]], [3, 6, 15, [30, 13]
], [4, 8, 12, [24, 13]], [3, 6, 12, 18, [36, 13]], [4, 6, 8, 12, 16, 24, [48, 
13]], [3, 6, 9, 12, 18, 24, 36, [72, 13]]}, {[3, [21, 14]], [8, [16, 14]], [3,
12, [24, 14]], [4, 6, [24, 14]], [5, 10, [20, 14]], [3, 6, 9, [36, 14]]}, {[4,
[20, 15]], [6, [18, 15]], [3, 6, [30, 15]], [3, 9, [27, 15]], [4, 8, [24, 15]],
[3, 6, 12, [36, 15]], [6, 8, 12, [24, 15]], [3, 9, 12, 18, [36, 15]], [4, 6, 8,
12, 16, [48, 15]], [3, 6, 9, 12, 18, 24, [72, 15]]}, {[3, [24, 16]], [5, [20, 
16]], [9, [18, 16]], [4, 12, [24, 16]], [3, 6, 18, [36, 16]], [4, 6, 12, 18, [
36, 16]], [3, 6, 9, 18, 27, [54, 16]], [4, 6, 8, 12, 24, [48, 16]], [3, 6, 9, 
12, 18, 36, [72, 16]]}, {[6, 8, [24, 17]], [3, 9, 12, [36, 17]], [4, 6, 8, 16,
24, [48, 17]], [3, 6, 9, 12, 24, 36, [72, 17]]}, {[3, [27, 18]], [4, [24, 18]],
[7, [21, 18]], [10, [20, 18]], [3, 6, [36, 18]], [3, 15, [30, 18]], [6, 12, [24
, 18]], [3, 9, 18, [36, 18]], [4, 6, 12, [36, 18]], [4, 8, 16, [32, 18]], [3, 6
, 9, 18, [54, 18]], [3, 6, 12, 24, [48, 18]], [4, 6, 8, 12, [48, 18]], [3, 6, 9
, 12, 18, [72, 18]], [4, 6, 8, 12, 18, 24, 36, [72, 18]], [3, 6, 9, 12, 18, 27,
36, 54, [108, 18]]}, {[4, 14, [28, 19]], [8, 12, [24, 19]], [3, 6, 21, [42, 19]
], [3, 12, 18, [36, 19]], [4, 6, 18, [36, 19]], [5, 10, 15, [30, 19]], [3, 6, 9
, 27, [54, 19]], [4, 6, 8, 16, [48, 19]], [4, 8, 10, 20, [40, 19]], [3, 6, 9, 
12, 24, [72, 19]], [3, 6, 12, 15, 30, [60, 19]], [4, 6, 12, 16, 24, [48, 19]],
[3, 6, 9, 18, 24, 36, [72, 19]]}, {[3, [30, 20]], [5, [25, 20]], [6, [24, 20]],
[11, [22, 20]], [3, 9, [36, 20]], [4, 8, [32, 20]], [3, 6, 12, [48, 20]], [6, 
10, 15, [30, 20]], [4, 6, 8, 24, [48, 20]], [3, 6, 9, 12, 36, [72, 20]], [4, 6,
8, 12, 18, 24, [72, 20]], [3, 6, 9, 12, 18, 27, 36, [108, 20]]}, {[4, [28, 21]]
, [8, [24, 21]], [3, 6, [42, 21]], [3, 12, [36, 21]], [4, 6, [36, 21]], [5, 10,
[30, 21]], [3, 6, 9, [54, 21]], [4, 8, 10, [40, 21]], [3, 6, 12, 15, [60, 21]],
[4, 6, 12, 16, [48, 21]], [6, 9, 12, 18, [36, 21]], [3, 6, 9, 18, 24, [72, 21]]
, [4, 8, 12, 16, 24, [48, 21]], [3, 6, 12, 18, 24, 36, [72, 21]], [4, 6, 8, 12,
18, 36, [72, 21]], [3, 6, 9, 12, 18, 27, 54, [108, 21]], [4, 6, 8, 12, 16, 24,
32, 48, [96, 21]], [3, 6, 9, 12, 18, 24, 36, 48, 72, [144, 21]]}, {[3, [33, 22]
], [12, [24, 22]], [3, 18, [36, 22]], [4, 16, [32, 22]], [5, 15, [30, 22]], [6,
10, [30, 22]], [7, 14, [28, 22]], [3, 6, 24, [48, 22]], [3, 9, 15, [45, 22]], [
4, 6, 8, [48, 22]], [4, 12, 18, [36, 22]], [3, 6, 9, 12, [72, 22]], [3, 6, 18,
27, [54, 22]], [4, 6, 12, 24, [48, 22]], [3, 6, 9, 18, 36, [72, 22]], [4, 6, 8,
12, 24, 36, [72, 22]], [3, 6, 9, 12, 18, 36, 54, [108, 22]], [4, 6, 8, 12, 16,
18, 24, 36, 48, 72, [144, 22]], [3, 6, 9, 12, 18, 24, 27, 36, 54, 72, 108, [216
, 22]]}, {[6, 15, [30, 23]], [4, 8, 20, [40, 23]], [6, 9, 12, [36, 23]], [3, 6,
12, 30, [60, 23]], [4, 6, 16, 24, [48, 23]], [4, 8, 12, 16, [48, 23]], [3, 6, 9
, 24, 36, [72, 23]], [3, 6, 12, 18, 24, [72, 23]], [4, 6, 8, 12, 18, [72, 23]],
[3, 6, 9, 12, 18, 27, [108, 23]], [4, 6, 8, 12, 16, 24, 32, [96, 23]], [3, 6, 9
, 12, 18, 24, 36, 48, [144, 23]]}, {[3, [36, 24]], [4, [32, 24]], [5, [30, 24]]
, [7, [28, 24]], [9, [27, 24]], [13, [26, 24]], [3, 6, [48, 24]], [4, 12, [36,
24]], [3, 6, 18, [54, 24]], [4, 6, 12, [48, 24]], [4, 10, 20, [40, 24]], [6, 9,
18, [36, 24]], [3, 6, 9, 18, [72, 24]], [3, 6, 15, 30, [60, 24]], [4, 8, 12, 24
, [48, 24]], [3, 6, 12, 18, 36, [72, 24]], [4, 6, 8, 12, 24, [72, 24]], [3, 6,
9, 12, 18, 36, [108, 24]], [4, 6, 8, 18, 24, 36, [72, 24]], [3, 6, 9, 12, 27, 
36, 54, [108, 24]], [4, 6, 8, 12, 16, 24, 48, [96, 24]], [3, 6, 9, 12, 18, 24,
36, 72, [144, 24]], [4, 6, 8, 12, 16, 18, 24, 36, 48, [144, 24]], [3, 6, 9, 12,
18, 24, 27, 36, 54, 72, [216, 24]]}, {[6, [30, 25]], [3, 9, [45, 25]], [4, 8, [
40, 25]], [4, 18, [36, 25]], [10, 15, [30, 25]], [3, 6, 12, [60, 25]], [3, 6, 
27, [54, 25]], [4, 6, 16, [48, 25]], [6, 12, 18, [36, 25]], [3, 6, 9, 24, [72,
25]], [3, 9, 18, 27, [54, 25]], [4, 8, 16, 24, [48, 25]], [3, 6, 12, 24, 36, [
72, 25]], [4, 6, 8, 12, 36, [72, 25]], [4, 6, 12, 20, 30, [60, 25]], [6, 8, 12,
16, 24, [48, 25]], [3, 6, 9, 12, 18, 54, [108, 25]], [3, 6, 9, 18, 30, 45, [90,
25]], [3, 9, 12, 18, 24, 36, [72, 25]], [4, 6, 8, 12, 16, 32, 48, [96, 25]], [3
, 6, 9, 12, 18, 24, 48, 72, [144, 25]], [4, 6, 8, 12, 16, 18, 24, 36, 72, [144,
25]], [3, 6, 9, 12, 18, 24, 27, 36, 54, 108, [216, 25]]}, {[3, [39, 26]], [14,
[28, 26]], [3, 21, [42, 26]], [4, 10, [40, 26]], [6, 9, [36, 26]], [8, 16, [32,
26]], [3, 6, 15, [60, 26]], [3, 12, 24, [48, 26]], [4, 6, 24, [48, 26]], [4, 8,
12, [48, 26]], [5, 10, 20, [40, 26]], [3, 6, 9, 36, [72, 26]], [3, 6, 12, 18, [
72, 26]], [4, 6, 8, 18, 24, [72, 26]], [3, 6, 9, 12, 27, 36, [108, 26]], [4, 6,
8, 12, 16, 24, [96, 26]], [3, 6, 9, 12, 18, 24, 36, [144, 26]], [4, 6, 8, 12, 
16, 18, 24, 48, 72, [144, 26]], [3, 6, 9, 12, 18, 24, 27, 36, 72, 108, [216, 26
]]}, {[4, [36, 27]], [10, [30, 27]], [3, 6, [54, 27]], [3, 15, [45, 27]], [6, 
12, [36, 27]], [3, 9, 18, [54, 27]], [4, 8, 16, [48, 27]], [9, 12, 18, [36, 27]
], [3, 6, 12, 24, [72, 27]], [4, 6, 8, 12, [72, 27]], [4, 6, 12, 20, [60, 27]],
[4, 12, 16, 24, [48, 27]], [6, 8, 12, 16, [48, 27]], [3, 6, 9, 12, 18, [108, 27
]], [3, 6, 9, 18, 30, [90, 27]], [3, 6, 18, 24, 36, [72, 27]], [3, 9, 12, 18, 
24, [72, 27]], [4, 6, 8, 18, 36, [72, 27]], [3, 6, 9, 12, 27, 54, [108, 27]], [
4, 6, 8, 12, 16, 32, [96, 27]], [4, 6, 12, 18, 24, 36, [72, 27]], [3, 6, 9, 12,
18, 24, 48, [144, 27]], [3, 6, 9, 18, 27, 36, 54, [108, 27]], [4, 6, 8, 12, 24,
32, 48, [96, 27]], [3, 6, 9, 12, 18, 36, 48, 72, [144, 27]], [4, 6, 8, 12, 16,
18, 24, 36, [144, 27]], [3, 6, 9, 12, 18, 24, 27, 36, 54, [216, 27]]}, {[3, [42
, 28]], [5, [35, 28]], [8, [32, 28]], [15, [30, 28]], [3, 12, [48, 28]], [4, 6,
[48, 28]], [4, 20, [40, 28]], [5, 10, [40, 28]], [6, 18, [36, 28]], [3, 6, 9, [
72, 28]], [3, 6, 30, [60, 28]], [3, 9, 27, [54, 28]], [4, 8, 24, [48, 28]], [3,
6, 12, 36, [72, 28]], [4, 6, 12, 30, [60, 28]], [6, 8, 12, 24, [48, 28]], [3, 6
, 9, 18, 45, [90, 28]], [3, 9, 12, 18, 36, [72, 28]], [4, 6, 8, 24, 36, [72, 28
]], [3, 6, 9, 12, 36, 54, [108, 28]], [4, 6, 8, 12, 16, 48, [96, 28]], [3, 6, 9
, 12, 18, 24, 72, [144, 28]], [4, 6, 8, 12, 16, 18, 24, 48, [144, 28]], [3, 6,
9, 12, 18, 24, 27, 36, 72, [216, 28]], [4, 6, 8, 12, 16, 18, 36, 48, 72, [144,
28]], [3, 6, 9, 12, 18, 24, 27, 54, 72, 108, [216, 28]]}, {[9, 12, [36, 29]], [
4, 12, 16, [48, 29]], [8, 10, 20, [40, 29]], [3, 6, 18, 24, [72, 29]], [3, 12,
15, 30, [60, 29]], [4, 6, 8, 18, [72, 29]], [4, 8, 14, 28, [56, 29]], [6, 8, 16
, 24, [48, 29]], [3, 6, 9, 12, 27, [108, 29]], [3, 6, 12, 21, 42, [84, 29]], [3
, 9, 12, 24, 36, [72, 29]], [4, 6, 12, 18, 24, [72, 29]], [4, 10, 12, 20, 30, [
60, 29]], [3, 6, 9, 18, 27, 36, [108, 29]], [3, 6, 15, 18, 30, 45, [90, 29]], [
4, 6, 8, 12, 24, 32, [96, 29]], [3, 6, 9, 12, 18, 36, 48, [144, 29]], [4, 6, 8,
16, 24, 32, 48, [96, 29]], [3, 6, 9, 12, 24, 36, 48, 72, [144, 29]], [4, 6, 8,
12, 16, 18, 24, 72, [144, 29]], [3, 6, 9, 12, 18, 24, 27, 36, 108, [216, 29]]},
{[3, [45, 30]], [4, [40, 30]], [6, [36, 30]], [7, [35, 30]], [11, [33, 30]], [
16, [32, 30]], [3, 6, [60, 30]], [3, 9, [54, 30]], [3, 24, [48, 30]], [4, 8, [
48, 30]], [5, 20, [40, 30]], [9, 18, [36, 30]], [3, 6, 12, [72, 30]], [4, 6, 12
, [60, 30]], [4, 12, 24, [48, 30]], [6, 8, 12, [48, 30]], [6, 14, 21, [42, 30]]
, [3, 6, 9, 18, [90, 30]], [3, 6, 18, 36, [72, 30]], [3, 9, 12, 18, [72, 30]],
[4, 6, 8, 24, [72, 30]], [4, 6, 20, 30, [60, 30]], [3, 6, 9, 12, 36, [108, 30]]
, [3, 6, 9, 30, 45, [90, 30]], [4, 6, 8, 12, 16, [96, 30]], [4, 6, 12, 18, 36,
[72, 30]], [3, 6, 9, 12, 18, 24, [144, 30]], [3, 6, 9, 18, 27, 54, [108, 30]],
[4, 6, 8, 12, 24, 48, [96, 30]], [4, 8, 12, 18, 24, 36, [72, 30]], [6, 10, 12,
15, 20, 30, [60, 30]], [3, 6, 9, 12, 18, 36, 72, [144, 30]], [3, 6, 12, 18, 27,
36, 54, [108, 30]], [4, 6, 8, 12, 16, 18, 36, 48, [144, 30]], [3, 6, 9, 12, 18,
24, 27, 54, 72, [216, 30]], [4, 6, 8, 12, 16, 24, 36, 48, 72, [144, 30]], [3, 6
, 9, 12, 18, 24, 36, 54, 72, 108, [216, 30]], [4, 6, 8, 12, 16, 18, 24, 32, 36,
48, 72, 96, 144, [288, 30]], [3, 6, 9, 12, 18, 24, 27, 36, 48, 54, 72, 108, 144
, 216, [432, 30]]}, {[4, 22, [44, 31]], [8, 10, [40, 31]], [12, 18, [36, 31]],
[3, 6, 33, [66, 31]], [3, 12, 15, [60, 31]], [3, 18, 27, [54, 31]], [4, 8, 14,
[56, 31]], [4, 16, 24, [48, 31]], [6, 8, 16, [48, 31]], [7, 14, 21, [42, 31]],
[3, 6, 12, 21, [84, 31]], [3, 6, 24, 36, [72, 31]], [3, 9, 12, 24, [72, 31]], [
4, 6, 8, 36, [72, 31]], [4, 10, 12, 20, [60, 31]], [6, 12, 16, 24, [48, 31]], [
3, 6, 9, 12, 54, [108, 31]], [3, 6, 15, 18, 30, [90, 31]], [3, 9, 18, 24, 36, [
72, 31]], [4, 6, 12, 24, 36, [72, 31]], [3, 6, 9, 18, 36, 54, [108, 31]], [4, 6
, 8, 12, 32, 48, [96, 31]], [4, 6, 8, 16, 24, 32, [96, 31]], [4, 8, 10, 16, 20,
40, [80, 31]], [3, 6, 9, 12, 18, 48, 72, [144, 31]], [3, 6, 9, 12, 24, 36, 48,
[144, 31]], [3, 6, 12, 15, 24, 30, 60, [120, 31]], [4, 6, 8, 12, 16, 18, 24, [
144, 31]], [3, 6, 9, 12, 18, 24, 27, 36, [216, 31]], [4, 6, 8, 12, 16, 18, 36,
72, [144, 31]], [4, 6, 8, 12, 24, 30, 40, 60, [120, 31]], [3, 6, 9, 12, 18, 24,
27, 54, 108, [216, 31]], [3, 6, 9, 12, 18, 36, 45, 60, 90, [180, 31]], [4, 6, 8
, 12, 18, 24, 36, 48, 72, [144, 31]], [3, 6, 9, 12, 18, 27, 36, 54, 72, 108, [
216, 31]]}, {[3, [48, 32]], [5, [40, 32]], [9, [36, 32]], [17, [34, 32]], [4, 
12, [48, 32]], [6, 14, [42, 32]], [3, 6, 18, [72, 32]], [3, 9, 21, [63, 32]], [
4, 6, 20, [60, 32]], [6, 8, 24, [48, 32]], [3, 6, 9, 30, [90, 32]], [3, 9, 12,
36, [72, 32]], [4, 6, 12, 18, [72, 32]], [4, 10, 12, 30, [60, 32]], [3, 6, 9, 
18, 27, [108, 32]], [3, 6, 15, 18, 45, [90, 32]], [4, 6, 8, 12, 24, [96, 32]],
[4, 8, 12, 18, 24, [72, 32]], [6, 10, 12, 15, 20, [60, 32]], [3, 6, 9, 12, 18,
36, [144, 32]], [3, 6, 12, 18, 27, 36, [108, 32]], [4, 6, 8, 16, 24, 48, [96, 
32]], [3, 6, 9, 12, 24, 36, 72, [144, 32]], [4, 6, 8, 12, 16, 18, 48, 72, [144,
32]], [4, 6, 8, 12, 16, 24, 36, 48, [144, 32]], [3, 6, 9, 12, 18, 24, 27, 72, 
108, [216, 32]], [3, 6, 9, 12, 18, 24, 36, 54, 72, [216, 32]], [4, 6, 8, 12, 16
, 18, 24, 32, 36, 48, 72, 96, [288, 32]], [3, 6, 9, 12, 18, 24, 27, 36, 48, 54,
72, 108, 144, [432, 32]]}]

                        This took, 104882.519, seconds.