A319062 - OEIS

%I #24 Sep 30 2019 21:55:35

%S 19601,22049,54568,48149,57968,13543,52057,132857,101399,296449,67357,

%T 171793,132576,298117,3414284,84457,223568,296449,380827,4029059,

%U 14380864,85193,261593,338168,1096112,7040291,14461231,3727271,93493,282907,1098599,1761679

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

%e The array starts as follows:

%e      19601,    22049,    48149,    52057,    67357,    84457,    85193

%e      54568,    57968,   132857,   171793,   223568,   261593,   282907

%e      13543,   101399,   132576,   296449,   338168,  1098599,  1244324

%e     296449,   298117,   380827,  1096112,  1761679,  2498247,  2500716

%e    3414284,  4029059,  7040291, 10858059, 12249190, 17134811, 19603812

%e   14380864, 14461231, 18366174, 22811283, 26295533, 33674748, 34998229

%e    3727271, 27936608, 29998045, 31239565, 34998229, 45331852, 56029298

%t rows = 7; t = 4;

%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 &],

%t      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, 4, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==5, 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.

%Y Cf. analog for i = 0..t: A319059 (t=1), A319060 (t=2), A319061 (t=3), A319063 (t=5), A319064 (t=6), A319065 (t=7).

%K nonn,tabl

%O 1,1

%A _Felix Fröhlich_, Sep 09 2018