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

1,1

Links

Table of n, a(n) for n=1..27.

Example

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

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 *)

Prog

(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

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).

Sequence in context: A238233 A242327 A339535 * A344830 A015407 A204536

Adjacent sequences: A319060 A319061 A319062 * A319064 A319065 A319066

Keyword

nonn,tabl

Author

Felix Fröhlich, Sep 09 2018

Status

approved