A319064 - OEIS

%I #26 Oct 27 2019 11:25:01

%S 4486949,4651993,20950343,4941649,21184318,23250274,5571593,33538051,

%T 163075007,741652533,11903257,78868324,189850207,882345432,710808570,

%U 19397501,86892632,230695118,1528112512,5126829291,2380570527,19841257,111899224,421883318,1701241810

%N 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.

%e The array starts as follows:

%e     4486949,    4651993,    4941649,    5571593,   11903257,   19397501,   19841257

%e    20950343,   21184318,   33538051,   78868324,   86892632,  111899224,  126664001

%e    23250274,  163075007,  189850207,  230695118,  421883318,  422771099,  497941351

%e   741652533,  882345432, 1528112512, 1701241810, 1986592318, 2005090271, 2596285385

%e   710808570, 5126829291

%e   2380570527

%t rows = 6; t = 6;T = Table[lst = {}; b = 2;

%t    While[Length[lst] < rows - n + 1,

%t      p = Prime[n + Range[0, t]];

%t     If[AllTrue[PowerMod[b, (p - 1), p^2], # == 1 &],

%t      AppendTo[lst, b]]; b++];

%t    lst, {n, rows}];

%t T // TableForm (* Print the A(n,k) table *)

%t Flatten[Table[T[[j, i - j + 1]], {i, 1, rows}, {j, 1, i}]] (* _Robert Price_, Oct 03 2019 *)

%o (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))

%o array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))

%o array(5, 7) \\ print initial 5 rows and 7 columns of array

%Y Cf. A244249, A256236.

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

%K nonn,tabl

%O 1,1

%A _Felix Fröhlich_, Sep 11 2018