A319059 - OEIS

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 #27 Sep 30 2019 20:18:17

%S 17,37,26,53,82,18,73,107,68,148,89,118,99,215,239,109,143,226,362,

%T 360,249,125,199,276,606,485,577,423,145,224,293,717,596,653,653,28,

%U 161,226,324,753,606,868,2098,784,63,181,251,374,766,699,1520,2526,1921,571

%N 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 The array starts as follows:

%e 17, 37, 53, 73, 89, 109, 125, 145, 161, 181, 197, 217

%e 26, 82, 107, 118, 143, 199, 224, 226, 251, 307, 332, 343

%e 18, 68, 99, 226, 276, 293, 324, 374, 393, 557, 607, 618

%e 148, 215, 362, 606, 717, 753, 766, 1207, 1304, 1322, 1371, 1451

%e 239, 360, 485, 596, 606, 699, 844, 846, 995, 1330, 1371, 1451

%e 249, 577, 653, 868, 1520, 1948, 1958, 2098, 2178, 2446, 2536, 2850

%e 423, 653, 2098, 2526, 2889, 3180, 4270, 4400, 4625, 4755, 5416, 5531

%e 28, 784, 1921, 2234, 2293, 3004, 4233, 4566, 4631, 4762, 4938, 5353

%e 63, 571, 1545, 3304, 3585, 3969, 4204, 5420, 6995, 7583, 7765, 7805

%e 374, 1492, 2509, 3323, 3405, 4472, 5651, 6154, 6492, 7805, 12348, 13040

%e 117, 1693, 2157, 4431, 4688, 6154, 6728, 6844, 6962, 9089, 11533, 13689

%e 787, 1368, 3214, 4106, 4895, 5552, 5830, 5900, 8892, 9229, 11389, 14272

%e 2059, 2152, 5548, 8354, 10557, 14368, 20320, 27657, 29296, 29945, 31434, 31452

%e 1085, 1771, 2210, 17902, 18793, 19679, 23670, 23676, 24298, 24928, 25885, 31800

%e 655, 1586, 1914, 3330, 3818, 7772, 8765, 9436, 9459, 12087, 13183, 24501

%t rows = 10; t = 1;

%t T = Table[lst = {}; b = 2;

%t While[Length[lst] < rows,

%t p = Prime[n + Range[0, t]];

%t If[AllTrue[PowerMod[b, (p - 1), p^2], # == 1 &], AppendTo[lst, b]]; b++];

%t lst, {n, rows}];

%t T // TableForm (* Print the A(n,k) table *)

%t Flatten[Table[T[[j, i - j + 1]], {i, 1, rows}, {j, 1, i}]] (* _Robert Price_, Sep 30 2019 *)

%o (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 array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))

%o array(8, 10) \\ print initial 8 rows and 10 columns of array

%Y Cf. A244249, A256236, A259075 (column 1).

%Y 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 nonn,tabl

%O 1,1

%A _Felix Fröhlich_, Sep 09 2018