cp's OEIS Frontend

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.

%I A319065 #23 Oct 27 2019 11:25:19
%S A319065 126664001,133487693,230695118,141313157,633266299,882345432,
%T A319065 236176001,1221760151,1986592318,12106746963,242883757,1575527851,
%U A319065 2715632968,12709975396,93732236423,356977349,1881738424,3726163057,38456038702,122728381675,66888229817
%N 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.
%e A319065 The array starts as follows:
%e A319065    126664001,    133487693,    141313157,   236176001,  242883757,  356977349, 358254649
%e A319065   230695118,    633266299,   1221760151,  1575527851, 1881738424, 2118321224
%e A319065   882345432,   1986592318,   2715632968,  3726163057, 5229752849
%e A319065 12106746963,  12709975396,  38456038702, 66479920578
%e A319065 93732236423, 122728381675, 143904477566
%e A319065 66888229817,  79246182226
%e A319065 84391291750
%t A319065 rows = 7; t = 7;
%t A319065 T = Table[lst = {}; b = 2;
%t A319065    While[Length[lst] < rows - n + 1,
%t A319065     fnd = True;
%t A319065     For[i = 0, i <= t, i++,
%t A319065      p = Prime[n + i];
%t A319065      If[PowerMod[b, (p - 1), p^2] != 1 , fnd = False;  Break[]]];
%t A319065     If[fnd, AppendTo[lst, b]]; b++];
%t A319065    lst, {n, rows}];
%t A319065 T // TableForm (* Print the A(n,k) table *)
%t A319065 Flatten[Table[T[[j, i - j + 1]], {i, 1, rows}, {j, 1, i}]] (* _Robert Price_, Oct 07 2019 *)
%o A319065 (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 A319065 array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
%o A319065 array(3, 3) \\ print initial 3 rows and 3 columns of array
%Y A319065 Cf. A244249, A256236.
%Y A319065 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 A319065 nonn,tabl,more
%O A319065 1,1
%A A319065 _Felix Fröhlich_, Sep 12 2018
%E A319065 a(7)-a(21) from _Robert Price_, Oct 07 2019