A258787 - OEIS

%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