A167289 Signature sequence of the smallest Salem number of degree 18 (A219300).

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, 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, 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

Offset: 1

Author

Roger L. Bagula, Nov 01 2009

Keywords

• nonn
• less

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Michael Mossinghoff, Lehmer's Problem Website.
• Michael Mossinghoff, Small Salem Numbers.
• Eric Weisstein's World of Mathematics, Signature Sequence.
• Index entries for sequences related to signature sequences

Crossrefs

Cf. A073011, A147851, A219300.

Programs

Mathematica

a = {1, -1, 1, -1, 0, 0, -1, 1, -1};
b = Join[a, {1}, Reverse[a]];
p[x_] = Sum[b[[n]]*x^(n - 1), {n, 1, Length[b]}];
m = Root[p[x], 2];
Take[Transpose[Sort[Flatten[Table[{i + j*m, i}, {i, 25}, {j, 17}], 1], #1[[1]] < #2[[1]] &]][[2]], 95]