A319060 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..2, with k running over the positive integers; square array, read by antidiagonals, downwards.

449, 557, 226, 593, 557, 1207, 649, 901, 1451, 606, 701, 1126, 2743, 1371, 3469, 757, 1207, 2774, 1451, 5938, 653, 793, 1243, 3657, 1667, 7624, 2098, 5649, 901, 1324, 4232, 2175, 11980, 4755, 10538, 26645, 1349, 1549, 4607, 2774, 12248, 5845, 11137, 35973

Offset: 1

Author

Felix Fröhlich, Sep 09 2018

Keywords

• nonn
• tabl

Examples

			The array starts as follows:
    449,   557,    593,    649,    701,    757,    793,    901,   1349,   1457
    226,   557,    901,   1126,   1207,   1243,   1324,   1549,   2224,   2449
   1207,  1451,   2743,   2774,   3657,   4232,   4607,   5176,   6682,   7251
    606,  1371,   1451,   1667,   2175,   2774,   4244,   8201,  13543,  13670
   3469,  5938,   7624,  11980,  12248,  13543,  17554,  20809,  23344,  24675
    653,  2098,   4755,   5845,  24314,  24675,  25876,  30270,  39016,  40133
   5649, 10538,  11137,  18049,  18710,  21426,  23158,  39016,  50902,  55134
  26645, 35973,  44710,  49556,  78991,  85972,  89283, 101540, 131466, 157641
   7805, 41854, 155349, 165407, 190906, 215029, 235210, 245586, 271376, 296832
   6154, 18488,  65788, 104520, 136463, 178863, 263429, 335829, 394854, 399254
		

Crossrefs

Cf. A244249, A256236.

Cf. analog for i = 0..t: A319059 (t=1), A319061 (t=3), A319062 (t=4), A319063 (t=5), A319064 (t=6), A319065 (t=7).

Programs

Mathematica

rows = 10; t = 2;
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, 2, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==3, 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