A258787 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.

5, 8, 17, 7, 26, 449, 30, 18, 197, 557, 3, 9, 118, 1207, 19601, 22, 146, 19, 361, 8201, 132857, 38, 40, 224, 249, 4625, 296449, 4486949, 54, 28, 68, 99, 4033, 4625, 296449, 126664001, 42, 130, 28, 118, 557, 8201, 997757, 24800401, 2363321449, 14, 41, 374, 1745, 901, 46826, 217682, 9312157, 758427193, 5229752849

Offset: 1

Author

Felix Fröhlich, Jun 10 2015

Keywords

• nonn
• tabl

Examples

			T(4, 3) = 197, because 197 is the smallest base b such that p = prime(4) = 7 is the 3rd base-b Wieferich prime.
Triangle T(n, k) starts:
  5;
  8,  17;
  7,  26,  449;
  30, 18,  197, 557;
  3,  9,   118, 1207, 19601;
  22, 146, 19,  361,  8201,  132857;
  38, 40,  224, 249,  4625,  296449, 4486949;
  54, 28,  68,  99,   4033,  4625,   296449,  126664001;
  42, 130, 28,  118,  557,   8201,   997757,  24800401,  2363321449;
		

Crossrefs

Cf. A256236 (diagonal). A286816.

Programs

PARI

nextwiefbase(n, a) = a++; while(Mod(a, n^2)^(n-1)!=1, a++); a
wiefrank(n, a) = i=0; forprime(p=1, n, if(Mod(a, p^2)^(p-1)==1, i++)); i
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++)
trianglerows(9) \\ print first nine rows of the triangle

Extensions

More terms from Max Alekseyev, Oct 14 2023