A256343 Moduli k for which A248218(k) = 3 (length of the terminating cycle of 0 under x -> x^2+1 modulo k).

5, 9, 15, 25, 27, 35, 45, 59, 63, 75, 95, 97, 105, 125, 135, 155, 171, 175, 177, 185, 189, 215, 225, 251, 279, 285, 291, 295, 315, 333, 375, 379, 387, 413, 419, 465, 475, 485, 513, 525, 531, 555, 617, 625, 645, 665, 675, 679, 753, 775, 785, 837, 855, 863, 873, 875, 885

Offset: 1

Author

M. F. Hasler, Mar 25 2015

Keywords

• nonn

Comments

All terms are odd. - Robert Israel, Dec 09 2020

If x is a term and y is a term of this sequence or A248219, then LCM(x,y) is a term. - Robert Israel, Mar 09 2021

Links

• Robert Israel, Table of n, a(n) for n = 1..7000

Crossrefs

Cf. A248218, A248219, A256342 - A256349, A003095, A247981.

Programs

Maple

f:= proc(n) local x, S, R,i;
  R:= Array(0..n,-1):
  R[0]:= 0: x:= 0;
  for i from 1 do
    x:= x^2+1 mod n;
    if R[x] >= 0 then return i - R[x] fi;
    R[x]:= i;
  od
end proc:
select(f=3, [seq(i,i=1..1000,2)]); # Robert Israel, Dec 09 2020

Mathematica

f[n_] := Module[{x, R, i}, R[_] = -1; R[0] = 0; x = 0; For[i = 1, True, i++, x = Mod[x^2+1, n]; If[R[x] >= 0, Return[i - R[x]]]; R[x] = i]];
Select[Table[i, {i, 1, 1000, 2}], f[#] == 3&] (* Jean-François Alcover, Feb 03 2023, after Robert Israel *)

PARI

for(i=1,900,A248218(i)==3&&print1(i","))