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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).

%I A353602 #6 Apr 29 2022 17:31:03
%S A353602 5,9,8,13,10,17,17,17,33,7,21,19,49,18,37,25,26,65,24,73,18,29,28,81,
%T A353602 26,109,19,65,33,35,97,32,145,30,129,80,37,37,113,43,181,31,193,82,
%U A353602 101,41,44,129,49,217,48,257,161,201,3,45,46,145,51,253,50,321,163
%N 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).
%e A353602 The array starts as follows:
%e A353602     5,   9,   13,   17,   21,   25,   29,   33,   37,   41,   45
%e A353602     8,  10,   17,   19,   26,   28,   35,   37,   44,   46,   53
%e A353602    17,  33,   49,   65,   81,   97,  113,  129,  145,  161,  177
%e A353602     7,  18,   24,   26,   32,   43,   49,   51,   57,   68,   74
%e A353602    37,  73,  109,  145,  181,  217,  253,  289,  325,  361,  397
%e A353602    18,  19,   30,   31,   48,   50,   67,   68,   79,   80,   97
%e A353602    65, 129,  193,  257,  321,  385,  449,  513,  577,  641,  705
%e A353602    80,  82,  161,  163,  242,  244,  323,  325,  404,  406,  485
%e A353602   101, 201,  301,  401,  501,  601,  701,  801,  901, 1001, 1101
%e A353602     3,   9,   27,   40,   81,   94,  112,  118,  120,  122,  124
%e A353602   145, 289,  433,  577,  721,  865, 1009, 1153, 1297, 1441, 1585
%o A353602 (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++)))
%o A353602 array(rows, cols) = for(x=2, rows+1, row(x, cols))
%o A353602 array(6, 5) \\ Print initial 6 rows and 5 columns of array
%o A353602 (Python)
%o A353602 def T(n, k):
%o A353602     j, n2, c = 2, n*n, 0
%o A353602     while c != k:
%o A353602         if pow(j, n-1, n2) == 1: c += 1
%o A353602         j += 1
%o A353602     return j-1
%o A353602 def auptodiag(maxd):
%o A353602     return [T(d+2-j, j) for d in range(1, maxd+1) for j in range(d, 0, -1)]
%o A353602 print(auptodiag(11)) # _Michael S. Branicky_, Apr 29 2022
%Y A353602 Cf. A185103 (column 1), A353600 (column 2).
%K A353602 nonn,tabl
%O A353602 2,1
%A A353602 _Felix Fröhlich_, Apr 29 2022