A319061 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..3, with k running over the positive integers; square array, read by antidiagonals, downwards.

557, 901, 1207, 1549, 4607, 1451, 2449, 5176, 2774, 13543, 4049, 10124, 8201, 42269, 24675, 5293, 19601, 13543, 91110, 45124, 39016, 5849, 20924, 24482, 91678, 95236, 302947, 217682, 6193, 22049, 30949, 101399, 188872, 387587, 928423, 165407, 7057, 26018

Offset: 1

Author

Felix Fröhlich, Sep 09 2018

Keywords

• nonn
• tabl

Examples

			The array starts as follows:
     557,    901,    1549,    2449,    4049,    5293,    5849,    6193
    1207,   4607,    5176,   10124,   19601,   20924,   22049,   26018
    1451,   2774,    8201,   13543,   24482,   30949,   31457,   40199
   13543,  42269,   91110,   91678,  101399,  132576,  142148,  210258
   24675,  45124,   95236,  188872,  236915,  273971,  296449,  298117
   39016, 302947,  387587,  609436,  637111,  962525, 1015033, 1074751
  217682, 928423, 1546225, 1666084, 1756986, 2105290, 2673538, 2733520
  165407, 215029, 1008933, 1370816, 1487743, 1493395, 1624207, 2998943
		

Crossrefs

Cf. A244249, A256236.

Cf. analog for i = 0..t: A319059 (t=1), A319060 (t=2), A319062 (t=4), A319063 (t=5), A319064 (t=6), A319065 (t=7).

Programs

Mathematica

rows = 8; t = 3;
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, 3, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==4, 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