A353602 Square array read by downward antidiagonals: A(n, k) = k-th Wieferich base of n, i.e., k-th b > 1 such that b^(n-1) == 1 (mod n^2).
5, 9, 8, 13, 10, 17, 17, 17, 33, 7, 21, 19, 49, 18, 37, 25, 26, 65, 24, 73, 18, 29, 28, 81, 26, 109, 19, 65, 33, 35, 97, 32, 145, 30, 129, 80, 37, 37, 113, 43, 181, 31, 193, 82, 101, 41, 44, 129, 49, 217, 48, 257, 161, 201, 3, 45, 46, 145, 51, 253, 50, 321, 163
Offset: 2
Examples
The array starts as follows:
5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45
8, 10, 17, 19, 26, 28, 35, 37, 44, 46, 53
17, 33, 49, 65, 81, 97, 113, 129, 145, 161, 177
7, 18, 24, 26, 32, 43, 49, 51, 57, 68, 74
37, 73, 109, 145, 181, 217, 253, 289, 325, 361, 397
18, 19, 30, 31, 48, 50, 67, 68, 79, 80, 97
65, 129, 193, 257, 321, 385, 449, 513, 577, 641, 705
80, 82, 161, 163, 242, 244, 323, 325, 404, 406, 485
101, 201, 301, 401, 501, 601, 701, 801, 901, 1001, 1101
3, 9, 27, 40, 81, 94, 112, 118, 120, 122, 124
145, 289, 433, 577, 721, 865, 1009, 1153, 1297, 1441, 1585
Programs
-
PARI
row(n, terms) = my(i=0); for(b=2, oo, if(i>=terms, print(""); break, if(Mod(b, n^2)^(n-1)==1, print1(b, ", "); i++))) array(rows, cols) = for(x=2, rows+1, row(x, cols)) array(6, 5) \\ Print initial 6 rows and 5 columns of array -
Python
def T(n, k): j, n2, c = 2, n*n, 0 while c != k: if pow(j, n-1, n2) == 1: c += 1 j += 1 return j-1 def auptodiag(maxd): return [T(d+2-j, j) for d in range(1, maxd+1) for j in range(d, 0, -1)] print(auptodiag(11)) # Michael S. Branicky, Apr 29 2022