Wieferich pairs and Barker sequences, II
Peter Borwein and Michael J. Mossinghoff

The 1371 values of u < 10^13 for which n = 4u^2 passes all known
requirements for the order of a circulant Hadamard matrix.

Each value of u is shown with its prime factorization.

11715 [3, 5, 11, 71]
82005 [3, 5, 7, 11, 71]
550605 [3, 5, 11, 47, 71]
3854235 [3, 5, 7, 11, 47, 71]
3877665 [3, 5, 11, 71, 331]
5418777 [3, 7, 13, 23, 863]
8515221 [3, 11, 13, 23, 863]
9031295 [5, 7, 13, 23, 863]
9047885 [5, 7, 11, 71, 331]
10975393 [11, 13, 23, 47, 71]
12663915 [3, 5, 11, 23, 47, 71]
14192035 [5, 11, 13, 23, 863]
16256331 [3, 3, 7, 13, 23, 863]
27093885 [3, 5, 7, 13, 23, 863]
27143655 [3, 5, 7, 11, 71, 331]
29549135 [5, 7, 11, 23, 47, 71]
32926179 [3, 11, 13, 23, 47, 71]
42576105 [3, 5, 11, 13, 23, 863]
54876965 [5, 11, 13, 23, 47, 71]
59606547 [3, 7, 11, 13, 23, 863]
76827751 [7, 11, 13, 23, 47, 71]
81281655 [3, 3, 5, 7, 13, 23, 863]
82880065 [5, 41, 83, 4871]
88647405 [3, 5, 7, 11, 23, 47, 71]
92805449 [11, 71, 331, 359]
99344245 [5, 7, 11, 13, 23, 863]
120503279 [13, 23, 467, 863]
164630895 [3, 5, 11, 13, 23, 47, 71]
178819641 [3, 3, 7, 11, 13, 23, 863]
182250255 [3, 5, 11, 47, 71, 331]
229623405 [3, 5, 11, 67, 20771]
230483253 [3, 7, 11, 13, 23, 47, 71]
278416347 [3, 11, 71, 331, 359]
298032735 [3, 5, 7, 11, 13, 23, 863]
361509837 [3, 13, 23, 467, 863]
384138755 [5, 7, 11, 13, 23, 47, 71]
425250595 [5, 7, 11, 47, 71, 331]
464027245 [5, 11, 71, 331, 359]
535787945 [5, 7, 11, 67, 20771]
556069735 [5, 13, 23, 431, 863]
604580691 [3, 11, 13, 23, 71, 863]
647120505 [3, 5, 31, 67, 20771]
743705655 [3, 5, 7, 11, 31, 20771]
778497629 [7, 13, 23, 431, 863]
818187315 [3, 5, 11, 71, 211, 331]
843522953 [7, 13, 23, 467, 863]
894098205 [3, 3, 5, 7, 11, 13, 23, 863]
1007634485 [5, 11, 13, 23, 71, 863]
1152416265 [3, 5, 7, 11, 13, 23, 47, 71]
1275751785 [3, 5, 7, 11, 47, 71, 331]
1325536069 [11, 13, 23, 467, 863]
1392081735 [3, 5, 11, 71, 331, 359]
1607363835 [3, 5, 7, 11, 67, 20771]
1668209205 [3, 5, 13, 23, 431, 863]
1948914429 [3, 7, 11, 71, 331, 359]
2134525327 [11, 23, 71, 331, 359]
2232101653 [83, 4871, 5521]
2289275765 [5, 7, 47, 67, 20771]
2335492887 [3, 7, 13, 23, 431, 863]
2372775185 [5, 11, 31, 67, 20771]
2403521885 [5, 29, 41, 83, 4871]
2530568859 [3, 7, 13, 23, 467, 863]
3022903455 [3, 5, 11, 13, 23, 71, 863]
3248190715 [5, 7, 11, 71, 331, 359]
3306431635 [5, 13, 31, 79, 20771]
3494595091 [13, 23, 29, 467, 863]
3632855083 [11, 13, 23, 47, 71, 331]
3892488145 [5, 7, 13, 23, 431, 863]
3976608207 [3, 11, 13, 23, 467, 863]
4097891705 [5, 31, 653, 40487]
4191755865 [3, 5, 11, 23, 47, 71, 331]
4217614765 [5, 7, 13, 23, 467, 863]
4232064837 [3, 7, 11, 13, 23, 71, 863]
4361856103 [11, 47, 71, 331, 359]
4528485893 [23, 83, 487, 4871]
4529843535 [3, 5, 7, 31, 67, 20771]
4736292495 [3, 5, 11, 71, 83, 4871]
4782199721 [13, 23, 43, 431, 863]
5004627615 [3, 3, 5, 13, 23, 431, 863]
5316048657 [3, 3, 3, 83, 487, 4871]
5341158795 [3, 5, 7, 31, 79, 20771]
5508404761 [101, 2903, 18787]
5727311205 [3, 5, 7, 11, 71, 211, 331]
6116767085 [5, 11, 13, 23, 431, 863]
6403575981 [3, 11, 23, 71, 331, 359]
6444923095 [5, 13, 31, 79, 40487]
6497392803 [3, 11, 83, 487, 4871]
6627680345 [5, 11, 13, 23, 467, 863]
6630809493 [3, 7, 11, 71, 83, 4871]
6696304959 [3, 83, 4871, 5521]
6867827295 [3, 5, 7, 47, 67, 20771]
7006478661 [3, 3, 7, 13, 23, 431, 863]
7053441395 [5, 7, 11, 13, 23, 71, 863]
7118325555 [3, 5, 11, 31, 67, 20771]
7543300215 [3, 5, 11, 31, 71, 20771]
7591706577 [3, 3, 7, 13, 23, 467, 863]
8072518331 [41, 83, 487, 4871]
8860081095 [3, 3, 5, 83, 487, 4871]
9278752483 [7, 11, 13, 23, 467, 863]
9327263439 [3, 13, 23, 863, 12049]
9616804015 [5, 7, 13, 43, 491531]
9744572145 [3, 5, 7, 11, 71, 331, 359]
9780763685 [5, 7, 11, 23, 47, 71, 331]
9919294905 [3, 5, 13, 31, 79, 20771]
10483785273 [3, 13, 23, 29, 467, 863]
10672626635 [5, 11, 23, 71, 331, 359]
10792300035 [3, 5, 11, 47, 67, 20771]
10828988005 [5, 11, 83, 487, 4871]
10898565249 [3, 11, 13, 23, 47, 71, 331]
11160508265 [5, 83, 4871, 5521]
11571085877 [13, 431, 863, 2393]
11677464435 [3, 5, 7, 13, 23, 431, 863]
11899555869 [3, 83, 4871, 9811]
12293675115 [3, 5, 31, 653, 40487]
12652844295 [3, 5, 7, 13, 23, 467, 863]
12696194511 [3, 3, 7, 11, 13, 23, 71, 863]
12747856485 [3, 5, 7, 13, 19, 491531]
13085568309 [3, 11, 47, 71, 331, 359]
13585457679 [3, 23, 83, 487, 4871]
14346599163 [3, 13, 23, 43, 431, 863]
16303261755 [3, 5, 11, 67, 71, 20771]
16525214283 [3, 101, 2903, 18787]
16609426295 [5, 7, 11, 31, 67, 20771]
16612175371 [11, 71, 179, 331, 359]
16824653195 [5, 7, 29, 41, 83, 4871]
17581277315 [5, 7, 19, 653, 40487]
18164275415 [5, 11, 13, 23, 47, 71, 331]
18350301255 [3, 5, 11, 13, 23, 431, 863]
19334769285 [3, 5, 13, 31, 79, 40487]
19492178409 [3, 3, 11, 83, 487, 4871]
19832593115 [5, 83, 4871, 9811]
19883041035 [3, 5, 11, 13, 23, 467, 863]
21160324185 [3, 5, 7, 11, 13, 23, 71, 863]
21763614691 [7, 13, 23, 863, 12049]
21809280515 [5, 11, 47, 71, 331, 359]
22565718255 [3, 5, 23, 47, 67, 20771]
22642429465 [5, 23, 83, 487, 4871]
23145021445 [5, 7, 13, 31, 79, 20771]
23910998605 [5, 13, 23, 43, 431, 863]
24217554993 [3, 41, 83, 487, 4871]
24462165637 [7, 13, 23, 29, 467, 863]
25182033415 [5, 7, 11, 47, 67, 20771]
25429985581 [7, 11, 13, 23, 47, 71, 331]
25690421757 [3, 7, 11, 13, 23, 431, 863]
26580243285 [3, 3, 3, 5, 83, 487, 4871]
27542023805 [5, 101, 2903, 18787]
27748829251 [11, 13, 23, 71, 331, 359]
27836257449 [3, 7, 11, 13, 23, 467, 863]
28077264007 [13, 23, 233, 467, 863]
28415292477 [3, 11, 13, 23, 47, 71, 863]
28491272843 [11, 71, 307, 331, 359]
28685241935 [5, 7, 31, 653, 40487]
28850412045 [3, 5, 7, 13, 43, 491531]
29342291055 [3, 5, 7, 11, 23, 47, 71, 331]
30414663735 [3, 5, 31, 47, 67, 20771]
30532992721 [7, 11, 47, 71, 331, 359]
32017879905 [3, 5, 11, 23, 71, 331, 359]
32486964015 [3, 5, 11, 83, 487, 4871]
33154047465 [3, 5, 7, 11, 71, 83, 4871]
33475398047 [7, 13, 23, 43, 431, 863]
33481524795 [3, 5, 83, 4871, 5521]
34199965943 [11, 13, 23, 863, 12049]
34518995081 [37, 83, 821, 13691]
34713257631 [3, 13, 431, 863, 2393]
35032393305 [3, 3, 5, 7, 13, 23, 431, 863]
37958532885 [3, 3, 5, 7, 13, 23, 467, 863]
38040944095 [5, 7, 11, 67, 71, 20771]
38440546001 [11, 13, 23, 29, 467, 863]
38454803805 [3, 5, 11, 47, 71, 211, 331]
38837598459 [3, 11, 41, 71, 83, 4871]
40362591655 [5, 41, 83, 487, 4871]
40756373037 [3, 3, 23, 83, 487, 4871]
41987849515 [5, 83, 4871, 20771]
42817369595 [5, 7, 11, 13, 23, 431, 863]
43039797489 [3, 3, 13, 23, 43, 431, 863]
44780931755 [5, 7, 19, 137, 491531]
44825031867 [3, 7, 11, 23, 71, 331, 359]
45114461665 [5, 7, 13, 31, 79, 40487]
46393762415 [5, 7, 11, 13, 23, 467, 863]
46636317195 [3, 5, 13, 23, 863, 12049]
47358820795 [5, 11, 13, 23, 47, 71, 863]
49813344823 [11, 23, 83, 487, 4871]
49828278885 [3, 5, 7, 11, 31, 67, 20771]
49836526113 [3, 11, 71, 179, 331, 359]
50473959585 [3, 5, 7, 29, 41, 83, 4871]
51338338019 [23, 83, 4871, 5521]
52331674285 [5, 11, 71, 331, 40487]
52604196931 [11, 13, 23, 43, 431, 863]
52653342595 [5, 7, 23, 47, 67, 20771]
52743831945 [3, 5, 7, 19, 653, 40487]
52803101505 [3, 5, 7, 11, 31, 71, 20771]
53272592165 [5, 13, 31, 653, 40487]
54492826245 [3, 5, 11, 13, 23, 47, 71, 331]
55050903765 [3, 3, 5, 11, 13, 23, 431, 863]
56709533595 [3, 5, 11, 13, 653, 40487]
57855429385 [5, 13, 431, 863, 2393]
58476535227 [3, 3, 3, 11, 83, 487, 4871]
58752746745 [3, 5, 7, 11, 31, 79, 20771]
58870316609 [13, 23, 83, 487, 4871]
59497779345 [3, 5, 83, 4871, 9811]
62242928815 [5, 41, 83, 751, 4871]
63480972555 [3, 3, 5, 7, 11, 13, 23, 71, 863]
65290844073 [3, 7, 13, 23, 863, 12049]
65427841545 [3, 5, 11, 47, 71, 331, 359]
66705402907 [11, 13, 23, 71, 331, 863]
67927288395 [3, 5, 23, 83, 487, 4871]
69435064335 [3, 5, 7, 13, 31, 79, 20771]
69664158985 [5, 17, 31, 653, 40487]
71732995815 [3, 5, 13, 23, 43, 431, 863]
72652664979 [3, 3, 41, 83, 487, 4871]
73386496911 [3, 7, 13, 23, 29, 467, 863]
73659354549 [3, 11, 83, 4871, 5521]
74158620855 [3, 5, 11, 17, 653, 40487]
74708386445 [5, 7, 11, 23, 71, 331, 359]
75546100245 [3, 5, 7, 11, 47, 67, 20771]
76289956743 [3, 7, 11, 13, 23, 47, 71, 331]
77071265271 [3, 3, 7, 11, 13, 23, 431, 863]
77859942395 [5, 19, 31, 653, 40487]
80997601139 [7, 13, 431, 863, 2393]
82626071415 [3, 5, 101, 2903, 18787]
82740966935 [5, 11, 23, 47, 67, 20771]
82883164485 [3, 5, 11, 19, 653, 40487]
83060876855 [5, 11, 71, 179, 331, 359]
83246487753 [3, 11, 13, 23, 71, 331, 359]
83508772347 [3, 3, 7, 11, 13, 23, 467, 863]
84231792021 [3, 13, 23, 233, 467, 863]
85473818529 [3, 11, 71, 307, 331, 359]
86055725805 [3, 5, 7, 31, 653, 40487]
88629852235 [5, 19, 83, 821, 13691]
88797701641 [11, 41, 83, 487, 4871]
89533936297 [13, 23, 467, 743, 863]
89727875545 [5, 7, 11, 47, 71, 211, 331]
91516167773 [41, 83, 4871, 5521]
91598978163 [3, 7, 11, 47, 71, 331, 359]
94113060899 [11, 13, 23, 71, 467, 863]
97460892045 [3, 3, 5, 11, 83, 487, 4871]
97784779105 [5, 13, 23, 47, 67, 20771]
100322690369 [11, 23, 47, 71, 331, 359]
100426194141 [3, 7, 13, 23, 43, 431, 863]
101802418523 [13, 4481, 1747591]
102599897829 [3, 11, 13, 23, 863, 12049]
103556985243 [3, 37, 83, 821, 13691]
104139772893 [3, 3, 13, 431, 863, 2393]
107288768495 [5, 23, 83, 821, 13691]
107999274935 [5, 19, 43, 653, 40487]
108818073455 [5, 7, 13, 23, 863, 12049]
109112243955 [3, 5, 11, 13, 31, 79, 20771]
109631565771 [3, 7, 13, 19, 43, 491531]
111042711087 [3, 7, 11, 29, 41, 83, 4871]
111520433695 [5, 11, 31, 47, 67, 20771]
114122832285 [3, 5, 7, 11, 67, 71, 20771]
115321638003 [3, 11, 13, 23, 29, 467, 863]
115804212069 [3, 7, 13, 863, 491531]
116430422563 [7, 13, 19, 137, 491531]
121087774965 [3, 5, 41, 83, 487, 4871]
122269119111 [3, 3, 3, 23, 83, 487, 4871]
122310828185 [5, 7, 13, 23, 29, 467, 863]
124081793129 [7, 19, 83, 821, 13691]
124182233587 [83, 409, 751, 4871]
125548336255 [5, 67, 18043, 20771]
125963548545 [3, 5, 83, 4871, 20771]
127149927905 [5, 7, 11, 13, 23, 47, 71, 331]
127281944647 [11, 13, 431, 863, 2393]
128452108785 [3, 5, 7, 11, 13, 23, 431, 863]
130385751845 [5, 31, 79, 263, 40487]
130895114559 [3, 11, 83, 4871, 9811]
134342795265 [3, 5, 7, 19, 137, 491531]
135230426265 [3, 5, 11, 31, 653, 40487]
135343384995 [3, 5, 7, 13, 31, 79, 40487]
137541691479 [3, 83, 151, 751, 4871]
138744146255 [5, 11, 13, 23, 71, 331, 359]
139181287245 [3, 5, 7, 11, 13, 23, 467, 863]
140226421335 [3, 5, 7, 11, 13, 19, 491531]
142076462385 [3, 5, 11, 13, 23, 47, 71, 863]
142456364215 [5, 11, 71, 307, 331, 359]
149440034469 [3, 11, 23, 83, 487, 4871]
152255167967 [7, 17, 19, 137, 491531]
152664963605 [5, 7, 11, 47, 71, 331, 359]
154015014057 [3, 23, 83, 4871, 5521]
156995022855 [3, 5, 11, 71, 331, 40487]
157812590793 [3, 11, 13, 23, 43, 431, 863]
157960027785 [3, 5, 7, 23, 47, 67, 20771]
159817776495 [3, 5, 13, 31, 653, 40487]
162627263543 [41, 83, 4871, 9811]
167376990235 [5, 7, 13, 23, 43, 431, 863]
168673505001 [3, 55889, 1006003]
169121562701 [7, 13, 19, 199, 491531]
170760547591 [31, 101, 2903, 18787]
170999829715 [5, 11, 13, 23, 863, 12049]
172594975405 [5, 37, 83, 821, 13691]
173566288155 [3, 5, 13, 431, 863, 2393]
176610949827 [3, 13, 23, 83, 487, 4871]
181764009205 [5, 97, 18043, 20771]
181777357113 [3, 11, 101, 2903, 18787]
182719276285 [5, 7, 13, 19, 43, 491531]
185667921613 [23, 41, 83, 487, 4871]
186728786445 [3, 5, 41, 83, 751, 4871]
187589028445 [5, 7, 13, 23, 863, 20771]
191253891665 [5, 41, 83, 821, 13691]
191657845613 [13, 157, 233, 467, 863]
192202730005 [5, 11, 13, 23, 29, 467, 863]
193007020115 [5, 7, 13, 863, 491531]
194187992295 [3, 5, 11, 41, 71, 83, 4871]
194241804757 [7, 11, 13, 23, 71, 331, 359]
195872532219 [3, 3, 7, 13, 23, 863, 12049]
196540848049 [7, 13, 23, 233, 467, 863]
198106162709 [7, 13, 43, 103, 491531]
198907047339 [3, 7, 11, 13, 23, 47, 71, 863]
199438909901 [7, 11, 71, 307, 331, 359]
200116208721 [3, 11, 13, 23, 71, 331, 863]
203781865185 [3, 3, 5, 23, 83, 487, 4871]
206317331467 [13, 53, 467, 743, 863]
207920510787 [3, 11, 1657, 1667, 2281]
208992476955 [3, 5, 17, 31, 653, 40487]
212682462135 [3, 5, 11, 13, 31, 79, 40487]
212902646145 [3, 5, 7, 31, 47, 67, 20771]
215198987445 [3, 3, 5, 13, 23, 43, 431, 863]
217376374429 [83, 233, 821, 13691]
217957994937 [3, 3, 3, 41, 83, 487, 4871]
220159490733 [3, 3, 7, 13, 23, 29, 467, 863]
221530919545 [5, 13, 31, 67, 79, 20771]
222605747265 [3, 5, 11, 47, 71, 83, 4871]
224125159335 [3, 5, 7, 11, 23, 71, 331, 359]
228556605095 [5, 7, 13, 19, 653, 40487]
228584033895 [3, 5, 7, 43, 103, 491531]
229236152465 [5, 83, 151, 751, 4871]
230437615811 [13, 19, 83, 821, 13691]
233179088635 [5, 23, 31, 47, 67, 20771]
233579827185 [3, 5, 19, 31, 653, 40487]
234103031599 [29, 41, 83, 487, 4871]
236035290689 [11, 23, 83, 821, 13691]
239399761601 [7, 11, 13, 23, 863, 12049]
242992803417 [3, 7, 13, 431, 863, 2393]
248222900805 [3, 5, 11, 23, 47, 67, 20771]
249066724115 [5, 11, 23, 83, 487, 4871]
249182630565 [3, 5, 11, 71, 179, 331, 359]
250489835475 [3, 5, 5, 11, 83, 751, 4871]
255806986799 [7, 7, 13, 19, 43, 491531]
256421455587 [3, 3, 11, 71, 307, 331, 359]
256691690095 [5, 23, 83, 4871, 5521]
259061905081 [7, 17, 43, 103, 491531]
259684566245 [5, 13, 23, 431, 467, 863]
260574277821 [3, 11, 13, 23, 71, 431, 863]
263020984655 [5, 11, 13, 23, 43, 431, 863]
265889556705 [3, 5, 19, 83, 821, 13691]
266134975171 [13, 23, 431, 863, 2393]
266393104923 [3, 11, 41, 83, 487, 4871]
268601808891 [3, 13, 23, 467, 743, 863]
269083822007 [7, 11, 13, 23, 29, 467, 863]
269183626635 [3, 5, 7, 11, 47, 71, 211, 331]
271863189213 [3, 7, 11, 41, 71, 83, 4871]
273353123209 [83, 293, 821, 13691]
274548503319 [3, 41, 83, 4871, 5521]
278950798087 [13, 23, 83, 821, 13691]
278965251015 [3, 5, 11, 31, 2903, 18787]
282339182697 [3, 11, 13, 23, 71, 467, 863]
282406981307 [11, 17, 71, 179, 331, 359]
292382676135 [3, 3, 3, 5, 11, 83, 487, 4871]
293354337315 [3, 5, 13, 23, 47, 67, 20771]
293729246085 [3, 5, 11, 71, 211, 331, 359]
294351583045 [5, 13, 23, 83, 487, 4871]
294782758985 [5, 11, 13, 23, 863, 20771]
294820162505 [5, 11, 23, 47, 71, 211, 331]
295554149583 [3, 7, 11, 19, 137, 491531]
298881714355 [5, 7, 17, 19, 653, 40487]
300968071107 [3, 11, 23, 47, 71, 331, 359]
301278582423 [3, 3, 7, 13, 23, 43, 431, 863]
302962261855 [5, 11, 101, 2903, 18787]
305407255569 [3, 13, 4481, 1747591]
308849904077 [11, 13, 23, 233, 467, 863]
309721298865 [3, 5, 11, 71, 653, 40487]
311214644075 [5, 5, 41, 83, 751, 4871]
311648046171 [3, 7, 11, 47, 71, 83, 4871]
313542563169 [3, 11, 71, 83, 331, 4871]
317354532495 [3, 5, 7, 11, 13, 43, 491531]
321331698489 [3, 17, 1657, 1667, 2281]
323733444695 [5, 31, 79, 653, 40487]
323997824805 [3, 5, 19, 43, 653, 40487]
326454220365 [3, 5, 7, 13, 23, 863, 12049]
331511745565 [5, 7, 11, 13, 23, 47, 71, 863]
333527014535 [5, 11, 13, 23, 71, 331, 863]
334561301085 [3, 5, 11, 31, 47, 67, 20771]
346534184645 [5, 11, 1657, 1667, 2281]
347412636207 [3, 3, 7, 13, 863, 491531]
348855682791 [3, 7, 11, 71, 179, 331, 359]
349291267689 [3, 7, 13, 19, 137, 491531]
354535110105 [3, 5, 11, 31, 47, 71, 20771]
357857639265 [3, 5, 7, 31, 67, 79, 20771]
359135427723 [3, 19, 1657, 1667, 2281]
363263324895 [3, 3, 5, 41, 83, 487, 4871]
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