A014423 From table of maximal epacts e(p) and corresponding primes p, for x_1=2, x_{m+1} = (x_m)^2+1; sequence gives e(p).

2, 3, 4, 6, 8, 12, 14, 18, 25, 28, 30, 32, 45, 55, 56, 76, 86, 89, 132, 142, 146, 150, 156, 168, 180, 196, 212, 228, 233, 252, 312, 429, 450, 532, 544, 561, 583, 706, 876, 992, 1168, 1383, 1415, 1428, 1534, 1560, 1638

Offset

1,1

References

R. K. Guy, How to factor a number, Proc. 5th Manitoba Conf. Numerical Math., Congress. Num. 16 (1975), 49-89.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..52

Mathematica

rec=Module[{r={}, maxe=0}, Do[seq={2}; e=0;
For[k=1, k<=p+1, k++, While[Length[seq]<2 k, AppendTo[seq, Mod[Last[seq]^2+1, p]]];
If[seq[[k]]===seq[[2 k]], e=k; Break[]]];
If[e>maxe, AppendTo[r, e]; maxe=e], {p, Prime/@Range[PrimePi[200000]]}]; r];
Print[StringJoin[Riffle[ToString/@rec, ", "]]] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(Magma) function RecordEpactsUpTo(N)
    rec := []; maxe := 0;
    for p in PrimesUpTo(N) do
        seq := [2 mod p]; e := 0;
        for k in [1..p+1] do
            while #seq lt 2*k do Append(~seq, (seq[#seq]^2 + 1) mod p); end while;
            if seq[k] eq seq[2*k] then e := k; break; end if;
        end for;
        if e gt maxe then Append(~rec, e); maxe := e; end if;
    end for;
    return rec;
end function;
rec := RecordEpactsUpTo(200000);
printf "%o\n", Join([IntegerToString(x) : x in rec], ", "); // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A014424.

Sequence in context: A275717 A029449 A028815 * A101902 A236912 A215966

Adjacent sequences: A014420 A014421 A014422 * A014424 A014425 A014426

Keyword

nonn

Author

N. J. A. Sloane

Status

approved