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A319060 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..2, with k running over the positive integers; square array, read by antidiagonals, downwards.

%I A319060 #24 Sep 30 2019 21:54:09
%S A319060 449,557,226,593,557,1207,649,901,1451,606,701,1126,2743,1371,3469,
%T A319060 757,1207,2774,1451,5938,653,793,1243,3657,1667,7624,2098,5649,901,
%U A319060 1324,4232,2175,11980,4755,10538,26645,1349,1549,4607,2774,12248,5845,11137,35973
%N A319060 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..2, with k running over the positive integers; square array, read by antidiagonals, downwards.
%e A319060 The array starts as follows:
%e A319060     449,   557,    593,    649,    701,    757,    793,    901,   1349,   1457
%e A319060     226,   557,    901,   1126,   1207,   1243,   1324,   1549,   2224,   2449
%e A319060    1207,  1451,   2743,   2774,   3657,   4232,   4607,   5176,   6682,   7251
%e A319060     606,  1371,   1451,   1667,   2175,   2774,   4244,   8201,  13543,  13670
%e A319060    3469,  5938,   7624,  11980,  12248,  13543,  17554,  20809,  23344,  24675
%e A319060     653,  2098,   4755,   5845,  24314,  24675,  25876,  30270,  39016,  40133
%e A319060    5649, 10538,  11137,  18049,  18710,  21426,  23158,  39016,  50902,  55134
%e A319060   26645, 35973,  44710,  49556,  78991,  85972,  89283, 101540, 131466, 157641
%e A319060    7805, 41854, 155349, 165407, 190906, 215029, 235210, 245586, 271376, 296832
%e A319060    6154, 18488,  65788, 104520, 136463, 178863, 263429, 335829, 394854, 399254
%t A319060 rows = 10; t = 2;
%t A319060 T = Table[lst = {}; b = 2;
%t A319060    While[Length[lst] < rows,
%t A319060      p = Prime[n + Range[0, t]];
%t A319060     If[AllTrue[PowerMod[b, (p-1), p^2], # == 1 &], AppendTo[lst, b]]; b++];
%t A319060    lst, {n, rows}];
%t A319060 T // TableForm (* Print the A(n,k) table *)
%t A319060 Flatten[Table[T[[j, i - j + 1]], {i, 1, rows}, {j, 1, i}]] (* _Robert Price_, Sep 30 2019 *)
%o A319060 (PARI) printrow(n, terms) = my(c=0); for(b=2, oo, my(j=0); for(i=0, 2, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==3, print1(b, ", "); c++); if(c==terms, break))
%o A319060 array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
%o A319060 array(8, 10) \\ print initial 8 rows and 10 columns of array
%Y A319060 Cf. A244249, A256236.
%Y A319060 Cf. analog for i = 0..t: A319059 (t=1), A319061 (t=3), A319062 (t=4), A319063 (t=5), A319064 (t=6), A319065 (t=7).
%K A319060 nonn,tabl
%O A319060 1,1
%A A319060 _Felix Fröhlich_, Sep 09 2018