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

1,1

Links

Table of n, a(n) for n=1..44.

Example

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

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 *)

Prog

(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

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).

Sequence in context: A107666 A020466 A142420 * A339532 A105376 A325083

Adjacent sequences: A319057 A319058 A319059 * A319061 A319062 A319063

Keyword

nonn,tabl

Author

Felix Fröhlich, Sep 09 2018

Status

approved