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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).
1
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
2,1
EXAMPLE
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
PROG
(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
CROSSREFS
Cf. A185103 (column 1), A353600 (column 2).
Sequence in context: A019754 A315120 A244249 * A123600 A063623 A085566
KEYWORD
nonn,tabl
AUTHOR
Felix Fröhlich, Apr 29 2022
STATUS
approved