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%I #13 Feb 16 2023 05:15:33
%S 3,4,6,8,10,12
%N Least crossing number of a prime knot with braid index n.
%e The trefoil knot 3_1 is the smallest prime knot with braid index 2, so a(2) = 3.
%e The figure-eight knot 4_1 is the smallest prime knot with braid index 3, so a(3) = 4.
%e The stevedore's knot 6_1 is the smallest prime knot with braid index 4, so a(4) = 6.
%e The smallest prime knots with braid index 5 are 8_1, 8_3, and 8_12, so a(5) = 8.
%e The smallest prime knots with braid index 6 are 10_1, 10_3, 10_13, 10_35, and 10_58, so a(6) = 10.
%e The smallest prime knots with braid index 7 are 12a_125, 12a_128, 12a_181, 12a_183, 12a_197, 12a_448, 12a_471, 12a_477, 12a_482, 12a_690, 12a_691, 12a_803, 12a_1124, 12a_1127, 12a_1166, 12a_1202, and 12a_1287 so a(7) = 12.
%Y Cf. A002863.
%K nonn,more
%O 2,1
%A _Charles R Greathouse IV_, Feb 14 2023