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, 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

Links

Table of n, a(n) for n=1..6.

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

Adjacent sequences: A307162 A307163 A307164 * A307166 A307167 A307168

Keyword

nonn,more,hard

Author

Alex Costea, Mar 27 2019

Status

approved