A244249 Table A(n,k) in which n-th row lists in increasing order all bases b to which p = prime(n) is a Wieferich prime (i.e., b^(p-1) is congruent to 1 mod p^2), read by antidiagonals.

5, 9, 8, 13, 10, 7, 17, 17, 18, 18, 21, 19, 24, 19, 3, 25, 26, 26, 30, 9, 19, 29, 28, 32, 31, 27, 22, 38, 33, 35, 43, 48, 40, 23, 40, 28, 37, 37, 49, 50, 81, 70, 65, 54, 28, 41, 44, 51, 67, 94, 80, 75, 62, 42, 14, 45, 46, 57, 68, 112, 89, 110, 68, 63, 41, 115

Offset: 1

Author

Felix Fröhlich, Jun 23 2014

Keywords

• nonn
• tabl

Examples

			Table starts with:
p =  2:   5,  9, 13, 17,  21,  25,  29,  33, ...
p =  3:   8, 10, 17, 19,  26,  28,  35,  37, ...
p =  5:   7, 18, 24, 26,  32,  43,  49,  51, ...
p =  7:  18, 19, 30, 31,  48,  50,  67,  68, ...
p = 11:   3,  9, 27, 40,  81,  94, 112, 118, ...
p = 13:  19, 22, 23, 70,  80,  89,  99, 146, ...
p = 17:  38, 40, 65, 75, 110, 131, 134, 155, ...
		

Links

• Alois P. Heinz, Rows n = 1..141, flattened

Crossrefs

Cf. A001220, A185103.

First column of table is A039678.

Main diagonal gives A280721.

Programs

Maple

A:= proc(n, k) option remember; local p, b;
      p:= ithprime(n);
      for b from 1 +`if`(k=1, 1, A(n, k-1))
        while b &^ (p-1) mod p^2<>1
      do od; b
    end:
seq(seq(A(n, 1+d-n), n=1..d), d=1..14);  # Alois P. Heinz, Jul 02 2014

Mathematica

A[n_, k_] := A[n, k] = Module[{p, b}, p = Prime[n]; For[b = 1 + If[k == 1, 1, A[n, k-1]], PowerMod[b, p-1, p^2] != 1, b++]; b]; Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 14}] // Flatten (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *)

PARI

forprime(p=2, 10^1, print1("p=", p, ": "); for(a=2, 10^2, if(Mod(a, p^2)^(p-1)==1, print1(a, ", "))); print(""))