A335507 Index of the least Wendt determinant (A048954) divisible by prime(n).

3, 2, 4, 3, 5, 28, 8, 9, 11, 7, 5, 9, 20, 14, 23, 13, 29, 15, 11, 35, 9, 13, 41, 11, 32, 25, 17, 53, 27, 28, 7, 13, 17, 23, 37, 15, 39, 27, 83, 43, 89, 45, 19, 32, 28, 11, 21, 37, 113, 19, 29, 34, 40, 25, 16, 131, 67, 15, 69, 35, 47, 73, 17, 31, 39, 79, 33, 21, 173, 29, 32, 179

Offset

1,1

Comments

It has been conjectured by Michael B Rees that there exists for every prime a Wendt determinant divisible by that prime. However the conjecture has been proved for all prime divisors equivalent to -1 (mod 6) - (see Lehmer link below).

Links

Table of n, a(n) for n=1..72.

Charles Helou, On Wendt's Determinant, Math. Comp., 66 (1997) No. 219, 1341-1346.

Emma Lehmer, On a Resultant Connected with Fermat's Last Theorem, Bull. Amer. Math. Soc. 41 (1935), 864-867.

Eric Weisstein's World of Mathematics, Circulant matrix.

Wikipedia, Circulant matrix.

Example

a(5) = 5 because Wendt(5) = 3751 = 11^2*131. It is divisible by prime(5) = 11 and Wendt(5) is the least Wendt determinant divisible by 11.

Mathematica

Wendt[n_]:=Module[{x}, Resultant[x^n-1, (1+x)^n-1, x]];
findW[n_]:= Module[{m=1}, While[!IntegerQ[Wendt[m]/n]||Mod[m, 6]==0, m++]; m];
Table[findW[Prime[n]], {n, 1, 100}]

Crossrefs

Cf. A048954.

Sequence in context: A243852 A025532 A329584 * A195459 A133131 A261985

Adjacent sequences: A335504 A335505 A335506 * A335508 A335509 A335510

Keyword

nonn

Author

Frank M Jackson and Michael B Rees, Jun 11 2020

Status

approved