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 A319062 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..4, with k running over the positive integers; square array, read by antidiagonals, downwards. 7

%I

%S 19601,22049,54568,48149,57968,13543,52057,132857,101399,296449,67357,

%T 171793,132576,298117,3414284,84457,223568,296449,380827,4029059,

%U 14380864,85193,261593,338168,1096112,7040291,14461231,3727271,93493,282907,1098599,1761679

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

%e The array starts as follows:

%e 19601, 22049, 48149, 52057, 67357, 84457, 85193

%e 54568, 57968, 132857, 171793, 223568, 261593, 282907

%e 13543, 101399, 132576, 296449, 338168, 1098599, 1244324

%e 296449, 298117, 380827, 1096112, 1761679, 2498247, 2500716

%e 3414284, 4029059, 7040291, 10858059, 12249190, 17134811, 19603812

%e 14380864, 14461231, 18366174, 22811283, 26295533, 33674748, 34998229

%e 3727271, 27936608, 29998045, 31239565, 34998229, 45331852, 56029298

%t rows = 7; t = 4;

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

%t While[Length[lst] < rows,

%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_, Sep 30 2019 *)

%o (PARI) printrow(n, terms) = my(c=0); for(b=2, oo, my(j=0); for(i=0, 4, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==5, print1(b, ", "); c++); if(c==terms, break))

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

%o array(8, 10) \\ print initial 8 rows and 10 columns of array

%Y Cf. A244249, A256236.

%Y Cf. analog for i = 0..t: A319059 (t=1), A319060 (t=2), A319061 (t=3), A319063 (t=5), A319064 (t=6), A319065 (t=7).

%K nonn,tabl

%O 1,1

%A _Felix FrÃ¶hlich_, Sep 09 2018

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Last modified June 19 21:16 EDT 2021. Contains 345149 sequences. (Running on oeis4.)