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A307165
Numbers k such that the sequence f(0)=f(1)=k, f(x)=(a*b) mod (a+b+1), where a=f(x-1) and b=f(x-2) is a cycle.
0
0, 1, 4, 16, 22, 340
OFFSET
1,3
COMMENTS
Zeros of A307087.
The next term, if it exists, is bigger than 1.5*10^7.
Abmod sequences are defined as follows: see A307087.
Abmod(x,y,0) = x;
Abmod(x,y,1) = y;
Abmod(x,y,n) = (a*b) mod (a+b+1), where a and b are the 2 previous terms: Abmod(x,y,n-2) and Abmod(x,y,n-1).
a(7) > 10^9 if it exists. - Bert Dobbelaere, Aug 18 2019
EXAMPLE
Abmod(4,4) is [4,4,7,4,4,7,4,4,7,...].
MATHEMATICA
cyclePos[s_] := Module[{sp = SequencePosition[s[[1 ;; -3]], s[[-2 ;; -1]]]}, If[Length[sp] == 0, 0, sp[[1, 1]]]]; a[n_] := Module[{f, g}, g[a_, b_] := Mod[a*b, a + b + 1]; f[0] = f[1] = n; f[k_] := f[k] = g[f[k - 1], f[k - 2]]; s = {}; m = 0; While[Length[s] < 4 || cyclePos[s] == 0, AppendTo[s, f[m]]; m++]; cyclePos[s] - 1]; seq = {}; Do[If[a[j] == 0, AppendTo[seq, j]], {j, 0, 340}]; seq (* Amiram Eldar, Jul 06 2019 *)
CROSSREFS
Cf. A307087.
Sequence in context: A237878 A065661 A100275 * A234275 A284810 A192199
KEYWORD
nonn,more,hard
AUTHOR
Alex Costea, Mar 27 2019
STATUS
approved