A244752 Square array read by antidiagonals in which rows are indexed by composite numbers w and row w gives n such that n^(w-1) == 1 (mod w^2).

17, 33, 37, 49, 73, 65, 65, 109, 129, 80, 81, 145, 193, 82, 101, 97, 181, 257, 161, 201, 145, 113, 217, 321, 163, 301, 289, 197, 129, 253, 385, 242, 401, 433, 393, 26, 145, 289, 449, 244, 501, 577, 589, 199, 257, 161, 325, 513, 323, 601, 721, 785, 224, 513

Offset

2,1

Comments

We can say that "w is a Wieferich pseudoprime to base n".

Any prime factor of w is a Wieferich prime to base n.

Links

Robert Price, Table of n, a(n) for n = 2..1276

Example

Table starts
w=4: 17, 33, 49, 65, 81, 97, 113, ....
w=6: 37, 73, 109, 145, 181, 217, ....
w=8: 65, 129, 193, 257, 321, 385, ....
w=9: 80, 82, 161, 163, 242, 244, ....
w=10: 101, 201, 301, 401, 501, 601, ....
w=12: 145, 289, 433, 577, 721, 865, ....
w=14: 197, 393, 589, 785, 981, ....
....

Mathematica

T = {};
For[w = 4, w <= 100, w++,
  If[PrimeQ[w], Continue[]];
  t = {};
  For [n = 2, n <= 10^5, n++,
   If[Mod[n^(w - 1), w^2] == 1, AppendTo[t, n]]];
  AppendTo[T, t]];
Print[TableForm[T]];
A244752 = {};
For[c = 1, c <= 50, c++,
  For[r = 1, r <= c, r++, AppendTo[A244752, T[[r]][[c - r + 1]]]]];
A244752 (* Robert Price, Sep 07 2019 *)

Prog

(PARI) forcomposite(w=2, 20, print1("w=", w, ": "); for(n=2, 10^3, if(Mod(n, w^2)^(w-1)==1, print1(n, ", "))); print(""))

Crossrefs

Cf. A001220, A240719, A244249.

Sequence in context: A336235 A085255 A283395 * A138393 A340000 A044062

Adjacent sequences: A244749 A244750 A244751 * A244753 A244754 A244755

Keyword

nonn,tabl

Author

Felix Fröhlich, Jul 05 2014

Extensions

a(17)-a(55) from Robert Price, Sep 07 2019

Status

approved