A319065 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..7, with k running over the positive integers; square array, read by antidiagonals, downwards.

126664001, 133487693, 230695118, 141313157, 633266299, 882345432, 236176001, 1221760151, 1986592318, 12106746963, 242883757, 1575527851, 2715632968, 12709975396, 93732236423, 356977349, 1881738424, 3726163057, 38456038702, 122728381675, 66888229817

Offset: 1

Author

Felix Fröhlich, Sep 12 2018

Keywords

• nonn
• tabl
• more

Examples

			The array starts as follows:
   126664001,    133487693,    141313157,   236176001,  242883757,  356977349, 358254649
  230695118,    633266299,   1221760151,  1575527851, 1881738424, 2118321224
  882345432,   1986592318,   2715632968,  3726163057, 5229752849
12106746963,  12709975396,  38456038702, 66479920578
93732236423, 122728381675, 143904477566
66888229817,  79246182226
84391291750
		

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), A319064 (t=6).

Programs

Mathematica

rows = 7; t = 7;
T = Table[lst = {}; b = 2;
   While[Length[lst] < rows - n + 1,
    fnd = True;
    For[i = 0, i <= t, i++,
     p = Prime[n + i];
     If[PowerMod[b, (p - 1), p^2] != 1 , fnd = False;  Break[]]];
    If[fnd, 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 07 2019 *)

PARI

printrow(n, terms) = my(c=0); for(b=2, oo, my(j=0); for(i=0, 7, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==8, print1(b, ", "); c++); if(c==terms, break))
array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
array(3, 3) \\ print initial 3 rows and 3 columns of array

Extensions

a(7)-a(21) from Robert Price, Oct 07 2019