A167289 - OEIS

%I #32 May 27 2024 11:40:46

%S 1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,6,5,4,3,2,1,7,6,5,4,3,2,8,1,7,6,5,4,3,

%T 9,2,8,1,7,6,5,4,10,3,9,2,8,1,7,6,5,11,4,10,3,9,2,8,1,7,6,12,5,11,4,

%U 10,3,9,2,8,1,7,13,6,12,5,11,4,10,3,9,2,8,14,1,7,13,6,12,5,11,4,10,3,9,15

%N Signature sequence of the smallest Salem number of degree 18 (A219300).

%H G. C. Greubel, <a href="/A167289/b167289.txt">Table of n, a(n) for n = 1..5000</a>

%H Michael Mossinghoff, <a href="http://wayback.cecm.sfu.ca/~mjm/Lehmer/">Lehmer's Problem Website</a>.

%H Michael Mossinghoff, <a href="http://wayback.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SignatureSequence.html">Signature Sequence</a>.

%H <a href="/index/Si#signature_sequences">Index entries for sequences related to signature sequences</a>

%t a = {1, -1, 1, -1, 0, 0, -1, 1, -1};

%t b = Join[a, {1}, Reverse[a]];

%t p[x_] = Sum[b[[n]]*x^(n - 1), {n, 1, Length[b]}];

%t m = Root[p[x], 2];

%t Take[Transpose[Sort[Flatten[Table[{i + j*m, i}, {i, 25}, {j, 17}], 1], #1[[1]] < #2[[1]] &]][[2]], 95]

%Y Cf. A073011, A147851, A219300.

%K nonn,less

%O 1,2

%A _Roger L. Bagula_, Nov 01 2009