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 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. 7

%I

%S 126664001,133487693,230695118,141313157,633266299,882345432,

%T 236176001,1221760151,1986592318,12106746963,242883757,1575527851,

%U 2715632968,12709975396,93732236423,356977349,1881738424,3726163057,38456038702,122728381675,66888229817

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

%e The array starts as follows:

%e 126664001, 133487693, 141313157, 236176001, 242883757, 356977349, 358254649

%e 230695118, 633266299, 1221760151, 1575527851, 1881738424, 2118321224

%e 882345432, 1986592318, 2715632968, 3726163057, 5229752849

%e 12106746963, 12709975396, 38456038702, 66479920578

%e 93732236423, 122728381675, 143904477566

%e 66888229817, 79246182226

%e 84391291750

%t rows = 7; t = 7;

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

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

%t fnd = True;

%t For[i = 0, i <= t, i++,

%t p = Prime[n + i];

%t If[PowerMod[b, (p - 1), p^2] != 1 , fnd = False; Break[]]];

%t If[fnd, 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 07 2019 *)

%o (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))

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

%o array(3, 3) \\ print initial 3 rows and 3 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), A319064 (t=6).

%K nonn,tabl,more

%O 1,1

%A _Felix FrÃ¶hlich_, Sep 12 2018

%E a(7)-a(21) from _Robert Price_, Oct 07 2019

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Last modified May 18 19:58 EDT 2021. Contains 344002 sequences. (Running on oeis4.)