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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
PARI
for(i=1,3000,A248218(i)==9&&print1(i","))
Comments