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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). 8

%I #32 Oct 28 2021 06:29:39

%S 17,33,37,49,73,65,65,109,129,80,81,145,193,82,101,97,181,257,161,201,

%T 145,113,217,321,163,301,289,197,129,253,385,242,401,433,393,26,145,

%U 289,449,244,501,577,589,199,257,161,325,513,323,601,721,785,224,513

%N 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).

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

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

%H Robert Price, <a href="/A244752/b244752.txt">Table of n, a(n) for n = 2..1276</a>

%e Table starts

%e w=4: 17, 33, 49, 65, 81, 97, 113, ....

%e w=6: 37, 73, 109, 145, 181, 217, ....

%e w=8: 65, 129, 193, 257, 321, 385, ....

%e w=9: 80, 82, 161, 163, 242, 244, ....

%e w=10: 101, 201, 301, 401, 501, 601, ....

%e w=12: 145, 289, 433, 577, 721, 865, ....

%e w=14: 197, 393, 589, 785, 981, ....

%e ....

%t T = {};

%t For[w = 4, w <= 100, w++,

%t If[PrimeQ[w], Continue[]];

%t t = {};

%t For [n = 2, n <= 10^5, n++,

%t If[Mod[n^(w - 1), w^2] == 1, AppendTo[t, n]]];

%t AppendTo[T, t]];

%t Print[TableForm[T]];

%t A244752 = {};

%t For[c = 1, c <= 50, c++,

%t For[r = 1, r <= c, r++, AppendTo[A244752, T[[r]][[c - r + 1]]]]];

%t A244752 (* _Robert Price_, Sep 07 2019 *)

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

%Y Cf. A001220, A240719, A244249.

%K nonn,tabl

%O 2,1

%A _Felix Fröhlich_, Jul 05 2014

%E a(17)-a(55) from _Robert Price_, Sep 07 2019

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)