Quote:
Originally Posted by mart_r
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Thank you very much. Very interesting read.
Here is a more complete table of First Occurrences. (It is easy to prove GAPS 2 mod 7 and 5 mod 7 do not exist.
There were a couple of mistakes in the previous table This is the corrected version
Note gaps like 2,5,9,12,16,19,23,26,30,33,37,40,44,47,51,54,58,61,65,68,72,75,79,82,86,89,93,96,100… and all 2 mod7 or 5 mod cannot exist.
Code:
GAP After Quadruple
1 1006301
3 11
4 1246241
6 3512051
7 1871
8 632081
10 1121831
11 15731
13 1481
14 1155611
15 1068251
17 18911
18 284741
20 12390011
21 191
22 821
24 3837131
25 875261
27 854921
28 10865291
29 18041
31 958541
32 680291
34 299471
35 1063961
36 663581
38 165701
39 2081
41 Unknown
42 21011
43 97841
45 79691
46 2223671
48 1022501
49 3436241
50 300491
52 294311
53 19421
55 Unknown
56 81041
57 463451
59 442571
60 419051
62 1902611
63 734471
64 6054281
66 16061
67 6332861
69 10037381
70 2246141
71 266681
73 3461
74 855731
76 67211
77 358901
78 7159511
80 2761721
81 77261
83 661091
84 1006331
85 257861
87 467471
88 13001
90 389561
91 69491
92 116531
94 2846861
95 594821
97 119291
98 1003361
99 11718821
101 22271
102 1230371
104 31721
105 2728541
106 1830341
108 1065011
109 5154761
111 654161
112 833711
113 Unknown
115 1627601
116 1912451
118 9585881
119 9431
120 295871
122 240041
123 5248091
125 22692611
126 5651
127 1023941
129 6880871
130 243701
132 2875331
133 51341
134 1798631
136 8557721
137 1588751
139 5201291
140 559211
141 62981
143 2541941
144 166841
146 397751
147 6556601
148 8827541
150 5234681
151 1122131
153 4575281
154 495611
155 354251
157 741751
158 2418671
160 Unknown
161 768191
162 13179581
164 1616801
165 1954361
167 Unknown
168 72221
169 19842671
171 1324571
172 Unknown
174 Unkown
175 2413421
176 2002331
178 14912741
179 978071
181 Unknown
182 340931
183 Unknown
185 14877671
186 Unknown
188 1791731
189 2136131
190 1508621
192 195731
193 1904471
195 6187451
196 1157831
197 Unknown
199 4734671
200 823721
The largest gap I've found is 5261 after 21872441