n = 1 mod 4, 5 <= n <= 20001: 4930 have a 2-bridge knot with |sigma| = 4;
no such 2-bridge knot for 70 values: [9, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1849, 2025, 2209, 2401, 2601, 2809, 3025, 3249, 3481, 3721, 3969, 4225, 4489, 4761, 5041, 5329, 5625, 5929, 6241, 6561, 6889, 7225, 7569, 7921, 8281, 8649, 9025, 9409, 9801, 10201, 10609, 11025, 11449, 11881, 12321, 12769, 13225, 13689, 14161, 14641, 15129, 15625, 16129, 16641, 17161, 17689, 18225, 18769, 19321, 19881]
these are exactly the odd squares in range: True
largest first-hit q: 106 at n = 16185
first hits for n <= 101: {5: 4, 9: None, 13: 4, 17: 6, 21: 4, 25: None, 29: 4, 33: 10, 37: 4, 41: 6, 45: 4, 49: None, 53: 4, 57: 10, 61: 4, 65: 6, 69: 4, 73: 10, 77: 4, 81: None, 85: 4, 89: 6, 93: 4, 97: 10, 101: 4}
python3 twobridge_scan.py 20001  29.67s user 0.37s system 99% cpu 30.062 total
