A319063 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..5, with k running over the positive integers; square array, read by antidiagonals, downwards.

132857, 171793, 2006776, 261593, 3091832, 296449, 618301, 3420818, 9654224, 17134811, 700993, 3524932, 11002557, 23250274, 36763941, 997757, 4108582, 16616568, 26073470, 195603158, 34998229, 1211201, 4349699, 20512643, 26646377, 307849316, 71724464

Offset: 1

Author

Felix Fröhlich, Sep 09 2018

Keywords

• nonn
• tabl

Examples

			The array starts as follows:
    132857,    171793,    261593,    618301,    700993,    997757,   1211201
   2006776,   3091832,   3420818,   3524932,   4108582,   4349699,   4416499
    296449,   9654224,  11002557,  16616568,  20512643,  20950343,  21184318
  17134811,  23250274,  26073470,  26646377,  44247410,  49287925,  49975689
  36763941, 195603158, 307849316, 364769263, 366974980, 395009864, 428594624
  34998229,  71724464, 124024853, 279238292, 709701384, 710808570
		

Crossrefs

Cf. A244249, A256236.

Cf. analog for i = 0..t: A319059 (t=1), A319060 (t=2), A319061 (t=3), A319062 (t=4), A319064 (t=6), A319065 (t=7).

Programs

Mathematica

rows = 6; t = 5;
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, Oct 01 2019 *)

PARI

printrow(n, terms) = my(c=0); for(b=2, oo, my(j=0); for(i=0, 5, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==6, print1(b, ", "); c++); if(c==terms, break))
array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
array(8, 8) \\ print initial 8 rows and 8 columns of array