%I #15 May 04 2024 14:55:40
%S 5,8,17,7,26,449,30,18,197,557,3,9,118,1207,19601,22,146,19,361,8201,
%T 132857,38,40,224,249,4625,296449,4486949,54,28,68,99,4033,4625,
%U 296449,126664001,42,130,28,118,557,8201,997757,24800401,2363321449,14,41,374,1745,901,46826,217682,9312157,758427193,5229752849
%N Triangle read by rows: T(n, k) = smallest base b > 1 such that p = prime(n) is the k-th base-b Wieferich prime for k = 1, 2, 3, ..., n.
%e T(4, 3) = 197, because 197 is the smallest base b such that p = prime(4) = 7 is the 3rd base-b Wieferich prime.
%e Triangle T(n, k) starts:
%e 5;
%e 8, 17;
%e 7, 26, 449;
%e 30, 18, 197, 557;
%e 3, 9, 118, 1207, 19601;
%e 22, 146, 19, 361, 8201, 132857;
%e 38, 40, 224, 249, 4625, 296449, 4486949;
%e 54, 28, 68, 99, 4033, 4625, 296449, 126664001;
%e 42, 130, 28, 118, 557, 8201, 997757, 24800401, 2363321449;
%o (PARI) nextwiefbase(n, a) = a++; while(Mod(a, n^2)^(n-1)!=1, a++); a
%o wiefrank(n, a) = i=0; forprime(p=1, n, if(Mod(a, p^2)^(p-1)==1, i++)); i
%o trianglerows(n) = i=1; while(i <= n, p=prime(i); for(k=1, i, b=2; while(wiefrank(p, b)!=k, b=nextwiefbase(p, b)); print1(b, ", ")); print(""); i++)
%o trianglerows(9) \\ print first nine rows of the triangle
%Y Cf. A256236 (diagonal). A286816.
%K nonn,tabl
%O 1,1
%A _Felix Fröhlich_, Jun 10 2015
%E More terms from _Max Alekseyev_, Oct 14 2023