A256349 Moduli n for which A248218(n) = 9.

81, 101, 271, 303, 361, 405, 505, 509, 567, 653, 707, 743, 813, 839, 909, 1033, 1083, 1187, 1355, 1447, 1515, 1527, 1539, 1753, 1805, 1897, 1919, 1959, 2025, 2121, 2229, 2381, 2439, 2511, 2517, 2525, 2527, 2545, 2579, 2687, 2727, 2749, 2753, 2777, 2803, 2835

Offset

1,1

Comments

If x is a member of this sequence, and y is a member of this sequence or A248219 or A256343, then LCM(x,y) is a member of this sequence. - Robert Israel, Mar 09 2021

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

In Z/81Z, the iteration of x -> x^2+1 starting at x = 0 yields (0, 1, 2, 5, 26, 29, 32, 53, 56, 59, 80, 2, ...), and m = 81 is the least positive number for which there is such a cycle of length 9, here [2, 5, 26, 29, 32, 53, 56, 59, 80], therefore a(1) = 81.

Maple

filter:= proc(n) local x, k, R, p;
  x:= 0; R[0]:= 0;
  for k from 1 do
    x:= x^2+1 mod n;
    if assigned(R[x]) then return evalb(k-R[x] = 9)
    else R[x]:= k
    fi
  od;
end proc:
select(filter, [$1..10000]); # Robert Israel, Mar 09 2021

Mathematica

filterQ[n_] := Module[{x, k, R}, x = 0; R[0] = 0; For[k = 1, True, k++, x = Mod[x^2 + 1, n]; If[IntegerQ[R[x]], Return[k - R[x] == 9], R[x] = k]]];
Select[Range[10000], filterQ] (* Jean-François Alcover, Feb 01 2023, after Robert Israel *)

Prog

(PARI) for(i=1, 3000, A248218(i)==9&&print1(i", "))

Crossrefs

Cf. A248218, A248219, A256342 - A256348, A003095, A247981.

Sequence in context: A117686 A104113 A102766 * A202002 A249613 A064828

Adjacent sequences: A256346 A256347 A256348 * A256350 A256351 A256352

Keyword

nonn

Author

M. F. Hasler, Mar 25 2015

Status

approved