A319062 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..4, with k running over the positive integers; square array, read by antidiagonals, downwards.

19601, 22049, 54568, 48149, 57968, 13543, 52057, 132857, 101399, 296449, 67357, 171793, 132576, 298117, 3414284, 84457, 223568, 296449, 380827, 4029059, 14380864, 85193, 261593, 338168, 1096112, 7040291, 14461231, 3727271, 93493, 282907, 1098599, 1761679

Offset

1,1

Links

Table of n, a(n) for n=1..32.

Example

The array starts as follows:
     19601,    22049,    48149,    52057,    67357,    84457,    85193
     54568,    57968,   132857,   171793,   223568,   261593,   282907
     13543,   101399,   132576,   296449,   338168,  1098599,  1244324
    296449,   298117,   380827,  1096112,  1761679,  2498247,  2500716
   3414284,  4029059,  7040291, 10858059, 12249190, 17134811, 19603812
  14380864, 14461231, 18366174, 22811283, 26295533, 33674748, 34998229
   3727271, 27936608, 29998045, 31239565, 34998229, 45331852, 56029298

Mathematica

rows = 7; t = 4;
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, 4, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==5, 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), A319060 (t=2), A319061 (t=3), A319063 (t=5), A319064 (t=6), A319065 (t=7).

Sequence in context: A093219 A184493 A339534 * A344829 A221333 A069369

Adjacent sequences: A319059 A319060 A319061 * A319063 A319064 A319065

Keyword

nonn,tabl

Author

Felix Fröhlich, Sep 09 2018

Status

approved