A340067 a(n) is the smallest k > 1 such that 2^n - 2 divides k^n - 1, for n > 1.

3, 7, 13, 31, 5, 127, 253, 511, 293, 2047, 1013, 8191, 375, 1885, 6945, 131071, 21905, 524287, 1048573, 202951, 1095249, 8388607, 2180425, 2784601, 1080599, 6046435, 23113817, 536870911, 23884363, 2147483647, 4294967293, 8589934591, 815291441, 2654752543, 19022463

Offset

2,1

Comments

All terms are odd.

Note that a(n) <= 2^n - 1.

If p is prime, then a(p) = 2^p - 1.

Links

Table of n, a(n) for n=2..36.

Formula

a(A000040(n)) = A001348(n).

Mathematica

a[n_] := Module[{k = 3, t = 2^n - 2}, While[PowerMod[k, n, t] != 1, k+=2]; k]; Array[a, 20, 2] (* Amiram Eldar, Jan 14 2021 *)

Crossrefs

Cf. A000040, A000918, A001348 (subsequence).

Sequence in context: A025249 A147098 A109291 * A199218 A062700 A330835

Adjacent sequences: A340064 A340065 A340066 * A340068 A340069 A340070

Keyword

nonn

Author

Thomas Ordowski, Jan 14 2021

Extensions

More terms from Amiram Eldar, Jan 14 2021

Status

approved