A319062 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.

19601, 22049, 54568, 48149, 57968, 13543, 52057, 132857, 101399, 296449, 67357, 171793, 132576, 298117, 3414284, 84457, 223568, 296449, 380827, 4029059, 14380864, 85193, 261593, 338168, 1096112, 7040291, 14461231, 3727271, 93493, 282907, 1098599, 1761679

Offset: 1

Author

Felix Fröhlich, Sep 09 2018

Keywords

• nonn
• tabl

Examples

			The array starts as follows:
     19601,    22049,    48149,    52057,    67357,    84457,    85193
     54568,    57968,   132857,   171793,   223568,   261593,   282907
     13543,   101399,   132576,   296449,   338168,  1098599,  1244324
    296449,   298117,   380827,  1096112,  1761679,  2498247,  2500716
   3414284,  4029059,  7040291, 10858059, 12249190, 17134811, 19603812
  14380864, 14461231, 18366174, 22811283, 26295533, 33674748, 34998229
   3727271, 27936608, 29998045, 31239565, 34998229, 45331852, 56029298
		

Crossrefs

Cf. A244249, A256236.

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

Programs

Mathematica

rows = 7; t = 4;
T = Table[lst = {}; b = 2;
   While[Length[lst] < rows,
     p = Prime[n + Range[0, t]];
    If[AllTrue[PowerMod[b, (p - 1), p^2], # == 1 &],
     AppendTo[lst, b]]; b++];
   lst, {n, rows}];
T // TableForm (* Print the A(n,k) table *)
Flatten[Table[T[[j, i - j + 1]], {i, 1, rows}, {j, 1, i}]] (* Robert Price, Sep 30 2019 *)

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))
array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
array(8, 10) \\ print initial 8 rows and 10 columns of array