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

1,1

Links

Table of n, a(n) for n=1..25.

Example

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

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 *)

Prog

(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

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).

Sequence in context: A350187 A015337 A339536 * A344831 A183679 A234793

Adjacent sequences: A319061 A319062 A319063 * A319065 A319066 A319067

Keyword

nonn,tabl

Author

Felix Fröhlich, Sep 11 2018

Status

approved