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

The top 19 known values of u < 5 * 10^24 for which n = 4u^2 cannot be
eliminated as a possible length of a Barker sequence.  The first is the
only value of u < 10^16.5, but it is possible that there are additional
permissible values of u between 10^16.5 and 5 * 10^24.  Each value of u is
shown with its prime factorization.

31540455528264605 [5, 13, 29, 41, 2953, 138200401]
66687671978077825 [5, 5, 53, 193, 4877, 53471161]
866939735715011725 [5, 5, 13, 53, 193, 4877, 53471161]
1293740836374709805 [5, 53, 97, 193, 4877, 53471161]
6468704181873549025 [5, 5, 53, 97, 193, 4877, 53471161]
16818630872871227465 [5, 13, 53, 97, 193, 4877, 53471161]
84093154364356137325 [5, 5, 13, 53, 97, 193, 4877, 53471161]
2487505958525418181705 [5, 29, 41, 2953, 1025273, 138200401]
6467515492166087272433 [13, 29, 41, 2953, 1025273, 138200401]
19417213258149231605065 [5, 17, 613, 1974353, 188748146801]
32337577460830436362165 [5, 13, 29, 41, 2953, 1025273, 138200401]
863383081390130269759645 [5, 41, 193, 2953, 53471161, 138200401]
1686504775565176744556405 [5, 13, 29, 41, 2953, 53471161, 138200401]
1890448348089674770182781 [53, 97, 4794006457, 76704103313]
2630496319975038327042325 [5, 5, 193, 24697, 53471161, 412835053]
2988996856098832119836165 [5, 13, 123397, 1974353, 188748146801]
3080894677428239302747085 [5, 5333, 612142549, 188748146801]
3770469237344599632723365 [5, 53, 97, 193, 4877, 2914393, 53471161]
4316915406950651348798225 [5, 5, 41, 193, 2953, 53471161, 138200401]