A319061 - OEIS

%I #27 Sep 30 2019 21:54:29

%S 557,901,1207,1549,4607,1451,2449,5176,2774,13543,4049,10124,8201,

%T 42269,24675,5293,19601,13543,91110,45124,39016,5849,20924,24482,

%U 91678,95236,302947,217682,6193,22049,30949,101399,188872,387587,928423,165407,7057,26018

%N 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.

%e The array starts as follows:

%e      557,    901,    1549,    2449,    4049,    5293,    5849,    6193

%e     1207,   4607,    5176,   10124,   19601,   20924,   22049,   26018

%e     1451,   2774,    8201,   13543,   24482,   30949,   31457,   40199

%e    13543,  42269,   91110,   91678,  101399,  132576,  142148,  210258

%e    24675,  45124,   95236,  188872,  236915,  273971,  296449,  298117

%e    39016, 302947,  387587,  609436,  637111,  962525, 1015033, 1074751

%e   217682, 928423, 1546225, 1666084, 1756986, 2105290, 2673538, 2733520

%e   165407, 215029, 1008933, 1370816, 1487743, 1493395, 1624207, 2998943

%t rows = 8; t = 3;

%t T = Table[lst = {}; b = 2;

%t    While[Length[lst] < rows,

%t      p = Prime[n + Range[0, t]];

%t     If[AllTrue[PowerMod[b,(p-1) p^2], #==1 &], AppendTo[lst, b]]; b++];

%t    lst, {n, rows}];

%t T // TableForm (* Print the A(n,k) table *)

%t Flatten[Table[T[[j, i - j + 1]], {i, 1, rows}, {j, 1, i}]] (* _Robert Price_, Sep 30 2019 *)

%o (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))

%o array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))

%o array(8, 10) \\ print initial 8 rows and 10 columns of array

%Y Cf. A244249, A256236.

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

%K nonn,tabl

%O 1,1

%A _Felix Fröhlich_, Sep 09 2018