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

2,1

Links

Table of n, a(n) for n=2..64.

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

Adjacent sequences: A353599 A353600 A353601 * A353603 A353604 A353605

Keyword

nonn,tabl

Author

Felix Fröhlich, Apr 29 2022

Status

approved