A319064 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..6, with k running over the positive integers; square array, read by antidiagonals, downwards.

4486949, 4651993, 20950343, 4941649, 21184318, 23250274, 5571593, 33538051, 163075007, 741652533, 11903257, 78868324, 189850207, 882345432, 710808570, 19397501, 86892632, 230695118, 1528112512, 5126829291, 2380570527, 19841257, 111899224, 421883318, 1701241810

Offset: 1

Author

Felix Fröhlich, Sep 11 2018

Keywords

• nonn
• tabl

Examples

			The array starts as follows:
    4486949,    4651993,    4941649,    5571593,   11903257,   19397501,   19841257
   20950343,   21184318,   33538051,   78868324,   86892632,  111899224,  126664001
   23250274,  163075007,  189850207,  230695118,  421883318,  422771099,  497941351
  741652533,  882345432, 1528112512, 1701241810, 1986592318, 2005090271, 2596285385
  710808570, 5126829291
  2380570527
		

Crossrefs

Cf. A244249, A256236.

Cf. analog for i = 0..t: A319059 (t=1), A319060 (t=2), A319061 (t=3), A319062 (t=4), A319063 (t=5), A319065 (t=7).

Programs

Mathematica

rows = 6; t = 6;T = Table[lst = {}; b = 2;
   While[Length[lst] < rows - n + 1,
     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 03 2019 *)

PARI

printrow(n, terms) = my(c=0); for(b=2, oo, my(j=0); for(i=0, 6, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==7, print1(b, ", "); c++); if(c==terms, break))
array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
array(5, 7) \\ print initial 5 rows and 7 columns of array