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

Author

Frank M Jackson and Michael B Rees, Jun 11 2020

Keywords

• nonn

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).

Examples

			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.
		

Links

• 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.

Crossrefs

Cf. A048954.

Programs

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}]