cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A335970 #17 Feb 16 2025 08:34:00
%S A335970 3,10,26,28,32,46,38,58,44,110,22,88,122,70,134,44,164,70,106,212,94,
%T A335970 70,146,128,208,62,142,116,310,56,94,212,86,280,320,262,316,82,110,
%U A335970 122,182,160,362,142,284,280,340,112,56,64,254,308,250,368,104,272,242,292,226
%N A335970 Index of the least Wendt determinant (A048954(k)) that is divisible by the least prime of the form k*prime(n) + 1.
%C A335970 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).
%H A335970 Gerard P. Michon, <a href="http://www.numericana.com/data/wendt.htm">Factorization of Wendt's Determinant</a> (table for n=1 to 114).
%H A335970 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CirculantMatrix.html">Circulant matrix</a>.
%H A335970 Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>.
%e A335970 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.
%t A335970 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
%Y A335970 Cf. A048954.
%K A335970 nonn
%O A335970 1,1
%A A335970 _Frank M Jackson_ and Michael B Rees, Jul 03 2020