A014424 From table of maximal epacts e(p) and corresponding primes p, for x_1=2, x_{m+1} = (x_m)^2+1; sequence gives p.

2, 5, 11, 17, 29, 47, 89, 109, 139, 229, 311, 331, 359, 521, 733, 797, 1459, 1669, 1747, 3359, 3467, 4327, 4679, 4793, 5323, 5867, 7229, 7919, 9421, 9649, 10103, 12809, 18439, 21911, 24043, 33311, 39799, 40529, 46751, 58111, 81517, 113933, 130399, 183581, 187181, 187217, 196543, 214213, 241907

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..62

Mathematica

RecordPrimesUpTo[N_]:=Module[{rec={}, 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[rec, p]; maxe=e], {p, Prime/@Range[PrimePi[N]]}]; rec];
RecordPrimesUpTo[100000] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(Magma) function RecordPrimesUpTo(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, p); maxe := e; end if;
    end for;
    return rec;
end function;
RecordPrimesUpTo(90000); // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A014423.

Sequence in context: A354789 A228353 A055499 * A023228 A027429 A336376

Adjacent sequences: A014421 A014422 A014423 * A014425 A014426 A014427

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Nov 26 2025

Status

approved