This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A206443 Least n such that L(n)<-1 and L(n)>L(n-1), where L(k) means the least root of the polynomial p(k,x) defined at A206284, and a(1)=13. 2
 13, 37, 145, 157, 181, 517, 565, 661, 2101, 2197, 2581, 2773, 8725, 8917, 10357, 10453, 10837, 35029, 35413, 41173, 41557, 43093, 43861 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A206074 gives an ordering {p(n,x)} of the polynomials with coefficients in {0,1}.  The least n for which p(n,x) has a root r less than -1 is 13, hence the choice of 13 as the initial term of A206443.  (Specifically, p(13,x)=1+x^2+x^3, and r=-1.46557...)  The next p(n,x) having a root less than -1 and >r is p(37,x)=1+x^2+x^5, with least root -1.1938... LINKS 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 *) CROSSREFS Cf. A206074, A206444. Sequence in context: A262755 A155300 A155252 * A155297 A181151 A155903 Adjacent sequences:  A206440 A206441 A206442 * A206444 A206445 A206446 KEYWORD nonn AUTHOR Clark Kimberling, Feb 07 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .