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%I #16 Oct 01 2020 02:40:46
%S 3,10,26,28,32,46,38,58,44,110,22,88,122,70,134,44,164,70,106,212,94,
%T 70,146,128,208,62,142,116,310,56,94,212,86,280,320,262,316,82,110,
%U 122,182,160,362,142,284,280,340,112,56,64,254,308,250,368,104,272,242,292,226
%N Index of the least Wendt determinant (A048954(k)) that is divisible by the least prime of the form k*prime(n) + 1.
%C 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CirculantMatrix.html">Circulant matrix</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>.
%e 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 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 Cf. A048954.
%K nonn
%O 1,1
%A _Frank M Jackson_ and Michael B Rees, Jul 03 2020
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