cp's OEIS Frontend

A319063 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..5, with k running over the positive integers; square array, read by antidiagonals, downwards.

%I A319063 #24 Oct 27 2019 11:24:33
%S A319063 132857,171793,2006776,261593,3091832,296449,618301,3420818,9654224,
%T A319063 17134811,700993,3524932,11002557,23250274,36763941,997757,4108582,
%U A319063 16616568,26073470,195603158,34998229,1211201,4349699,20512643,26646377,307849316,71724464
%N A319063 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..5, with k running over the positive integers; square array, read by antidiagonals, downwards.
%e A319063 The array starts as follows:
%e A319063     132857,    171793,    261593,    618301,    700993,    997757,   1211201
%e A319063    2006776,   3091832,   3420818,   3524932,   4108582,   4349699,   4416499
%e A319063     296449,   9654224,  11002557,  16616568,  20512643,  20950343,  21184318
%e A319063   17134811,  23250274,  26073470,  26646377,  44247410,  49287925,  49975689
%e A319063   36763941, 195603158, 307849316, 364769263, 366974980, 395009864, 428594624
%e A319063   34998229,  71724464, 124024853, 279238292, 709701384, 710808570
%t A319063 rows = 6; t = 5;
%t A319063 T = Table[lst = {}; b = 2;
%t A319063    While[Length[lst] < rows,
%t A319063      p = Prime[n + Range[0, t]];
%t A319063     If[AllTrue[PowerMod[b, (p - 1), p^2], # == 1 &],
%t A319063      AppendTo[lst, b]]; b++];
%t A319063    lst, {n, rows}];
%t A319063 T // TableForm (* Print the A(n,k) table *)
%t A319063 Flatten[Table[T[[j, i - j + 1]], {i, 1, rows}, {j, 1, i}]] (* _Robert Price_, Oct 01 2019 *)
%o A319063 (PARI) printrow(n, terms) = my(c=0); for(b=2, oo, my(j=0); for(i=0, 5, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==6, print1(b, ", "); c++); if(c==terms, break))
%o A319063 array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
%o A319063 array(8, 8) \\ print initial 8 rows and 8 columns of array
%Y A319063 Cf. A244249, A256236.
%Y A319063 Cf. analog for i = 0..t: A319059 (t=1), A319060 (t=2), A319061 (t=3), A319062 (t=4), A319064 (t=6), A319065 (t=7).
%K A319063 nonn,tabl
%O A319063 1,1
%A A319063 _Felix Fröhlich_, Sep 09 2018