A206444
Least n such that L(n)<-1 and L(n)A206284, and a(1)=13.
13, 53, 213, 853, 3413, 13653, 54613, 218453, 873813, 3495253
Offset: 1
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.
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Mathematica
highs := {First /@ #, Most[FoldList[Plus, 1, Length /@ #]]} &[Split[Rest[FoldList[Max, -\[Infinity], #]]]] & f[polyInX_] := {Min[#], Max[#]} &[ Map[#[[1]] &, DeleteCases[Map[{#, Head[#]} &, Chop[N[x /. Solve[polyInX == 0, x], 40]]], {_, Complex}]]] t = Table[IntegerDigits[n, 2], {n, 1, 100000}]; b[n_] := Reverse[Array[x^(# - 1) &, {n + 1}]] p[n_] := t[[n]].b[-1 + Length[t[[n]]]] Table[p[n], {n, 1, 25}] fitCriterion = Intersection[Map[#[[1]] &, DeleteCases[ Table[{n, Boole[IrreduciblePolynomialQ[p[n]]]}, {n, 1, #}], {_, 0}]], Map[#[[1]] &, DeleteCases[ Table[{n, CountRoots[#, {x, -Infinity, 0}] - CountRoots[#, {x, -1, 0}] &[p[n]]}, {n, 1, #}], {_, 0}]]] &[Length[t]]; polyNum = Map[{f[p[#]][[1]], #} &, fitCriterion]; up = Map[polyNum[[#]] &, highs[Map[#[[1]] &, polyNum]][[2]]] down = Map[polyNum[[#]] &, highs[Map[#[[1]] &, -polyNum]][[2]]] Table[up[[k, 2]], {k, 1, Length[up]}] (* A206443 *) Table[down[[k, 2]], {k, 1, Length[down]}] (* A206444 *) (* Peter J. C. Moses, Feb 06 2012 *)Extensions