A335970 Index of the least Wendt determinant (A048954(k)) that is divisible by the least prime of the form k*prime(n) + 1.

3, 10, 26, 28, 32, 46, 38, 58, 44, 110, 22, 88, 122, 70, 134, 44, 164, 70, 106, 212, 94, 70, 146, 128, 208, 62, 142, 116, 310, 56, 94, 212, 86, 280, 320, 262, 316, 82, 110, 122, 182, 160, 362, 142, 284, 280, 340, 112, 56, 64, 254, 308, 250, 368, 104, 272, 242, 292, 226

Offset

1,1

Comments

It has been conjectured by Michael B Rees that for every prime p there exists a Wendt determinant index j such that for all j < k primes of the form j*p + 1 will not divide Wendt(j). This sequence gives the least index k such that Wendt(k) is divisible by the least prime of the form k*p + 1 for each prime p = prime(n).

Links

Table of n, a(n) for n=1..59.

Gerard P. Michon, Factorization of Wendt's Determinant (table for n=1 to 114).

Eric Weisstein's World of Mathematics, Circulant matrix.

Wikipedia, Circulant matrix.

Example

a(2) = 10 gives k = 10, Wendt(10) = -210736858987743 = -1*3*11^9*31^3 and p = prime(2) = 3. Hence with k = 10 and p = 3, Wendt(k) is the least Wendt determinant divisible by the least prime of the form p*k + 1.

Mathematica

w[n_] := Module[{x}, Resultant[x^n-1, (1+x)^n-1, x]]; lst = {}; Do[q=1; While[Mod[q, 6]==0||!PrimeQ[r=1+Prime[n]*q]||!IntegerQ[w[q]/r], q++]; AppendTo[lst, q], {n, 1, 60}]; lst

Crossrefs

Cf. A048954.

Sequence in context: A299754 A190529 A343584 * A212967 A355902 A301410

Adjacent sequences: A335967 A335968 A335969 * A335971 A335972 A335973

Keyword

nonn

Author

Frank M Jackson and Michael B Rees, Jul 03 2020

Status

approved