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A319059 A(n, k) is the k-th number b > 1 such that b^(prime(n+i)-1) == 1 (mod prime(n+i)^2) for each i = 0..1, with k running over the positive integers; square array, read by antidiagonals, downwards.

%I A319059 #27 Sep 30 2019 20:18:17
%S A319059 17,37,26,53,82,18,73,107,68,148,89,118,99,215,239,109,143,226,362,
%T A319059 360,249,125,199,276,606,485,577,423,145,224,293,717,596,653,653,28,
%U A319059 161,226,324,753,606,868,2098,784,63,181,251,374,766,699,1520,2526,1921,571
%N A319059 A(n, k) is the k-th number b > 1 such that b^(prime(n+i)-1) == 1 (mod prime(n+i)^2) for each i = 0..1, with k running over the positive integers; square array, read by antidiagonals, downwards.
%e A319059 The array starts as follows:
%e A319059     17,   37,   53,    73,    89,   109,   125,   145,   161,   181,   197,   217
%e A319059     26,   82,  107,   118,   143,   199,   224,   226,   251,   307,   332,   343
%e A319059     18,   68,   99,   226,   276,   293,   324,   374,   393,   557,   607,   618
%e A319059    148,  215,  362,   606,   717,   753,   766,  1207,  1304,  1322,  1371,  1451
%e A319059    239,  360,  485,   596,   606,   699,   844,   846,   995,  1330,  1371,  1451
%e A319059    249,  577,  653,   868,  1520,  1948,  1958,  2098,  2178,  2446,  2536,  2850
%e A319059    423,  653, 2098,  2526,  2889,  3180,  4270,  4400,  4625,  4755,  5416,  5531
%e A319059     28,  784, 1921,  2234,  2293,  3004,  4233,  4566,  4631,  4762,  4938,  5353
%e A319059     63,  571, 1545,  3304,  3585,  3969,  4204,  5420,  6995,  7583,  7765,  7805
%e A319059    374, 1492, 2509,  3323,  3405,  4472,  5651,  6154,  6492,  7805, 12348, 13040
%e A319059    117, 1693, 2157,  4431,  4688,  6154,  6728,  6844,  6962,  9089, 11533, 13689
%e A319059    787, 1368, 3214,  4106,  4895,  5552,  5830,  5900,  8892,  9229, 11389, 14272
%e A319059   2059, 2152, 5548,  8354, 10557, 14368, 20320, 27657, 29296, 29945, 31434, 31452
%e A319059   1085, 1771, 2210, 17902, 18793, 19679, 23670, 23676, 24298, 24928, 25885, 31800
%e A319059    655, 1586, 1914,  3330,  3818,  7772,  8765,  9436,  9459, 12087, 13183, 24501
%t A319059 rows = 10; t = 1;
%t A319059 T = Table[lst = {}; b = 2;
%t A319059    While[Length[lst] < rows,
%t A319059     p = Prime[n + Range[0, t]];
%t A319059     If[AllTrue[PowerMod[b, (p - 1), p^2], # == 1 &], AppendTo[lst, b]]; b++];
%t A319059    lst, {n, rows}];
%t A319059 T // TableForm (* Print the A(n,k) table *)
%t A319059 Flatten[Table[T[[j, i - j + 1]], {i, 1, rows}, {j, 1, i}]] (* _Robert Price_, Sep 30 2019 *)
%o A319059 (PARI) printrow(n, terms) = my(c=0); for(b=2, oo, my(j=0); for(i=0, 1, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==2, print1(b, ", "); c++); if(c==terms, break))
%o A319059 array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
%o A319059 array(8, 10) \\ print initial 8 rows and 10 columns of array
%Y A319059 Cf. A244249, A256236, A259075 (column 1).
%Y A319059 Cf. analog for i = 0..t: A319060 (t=2), A319061 (t=3), A319062 (t=4), A319063 (t=5), A319064 (t=6), A319065 (t=7).
%K A319059 nonn,tabl
%O A319059 1,1
%A A319059 _Felix Fröhlich_, Sep 09 2018