OFFSET
1,2
COMMENTS
T(n, k) = T(n, k-1) if p is a base-k Wieferich prime.
A necessary condition for the failure of the first case of Fermat's last theorem for a prime p with prime index i is T(i, k) = 0 for k = 2..113 (cf. Suzuki, 1994).
LINKS
J. Suzuki, On the generalized Wieferich criteria, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 70, No. 7 (1994), 230-234.
FORMULA
T(n, 2) = A196202(n)-1.
EXAMPLE
The array starts as follows:
1, 3, 6, 6, 7, 9, 12, 12, 13, 15, 18
3, 11, 17, 23, 31, 34, 34, 42, 42, 45, 53
15, 20, 25, 49, 69, 69, 89, 99, 123, 138, 148
14, 56, 84, 126, 133, 181, 223, 258, 265, 279, 300
55, 55, 165, 242, 297, 319, 363, 363, 374, 494, 604
39, 143, 221, 234, 377, 494, 611, 650, 702, 832, 845
221, 391, 544, 748, 850, 901, 986, 1037, 1173, 1326, 1360
57, 399, 513, 741, 779, 1026, 1197, 1520, 1805, 1843, 1938
391, 782, 1035, 1357, 1610, 1886, 2001, 2254, 2438, 2599, 2714
29, 464, 522, 870, 1334, 2146, 2233, 2262, 2639, 3306, 3799
186, 713, 1085, 1364, 2077, 2883, 3441, 3534, 3999, 4123, 5022
37, 703, 777, 1776, 2479, 3589, 3700, 5032, 6068, 6512, 7252
PROG
(PARI) t(n, k) = my(p=prime(n)); sum(b=2, k, lift(Mod(b, p^2)^(p-1)-1))
array(rows, cols) = for(x=1, rows, for(y=2, cols+1, print1(t(x, y), ", ")); print(""))
array(11, 12) \\ Print initial 11 rows and 12 columns of array
CROSSREFS
KEYWORD
AUTHOR
Felix Fröhlich, Dec 08 2020
STATUS
approved