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

1,1

Links

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

Example

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, ...

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 *)

Prog

(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(""))

Crossrefs

Cf. A001220, A185103.

First column of table is A039678.

Main diagonal gives A280721.

Sequence in context: A077771 A019754 A315120 * A353602 A123600 A063623

Adjacent sequences: A244246 A244247 A244248 * A244250 A244251 A244252

Keyword

nonn,tabl

Author

Felix Fröhlich, Jun 23 2014

Status

approved