A102375 Decimal expansion of reciprocal of the smallest positive zero of sum_{j>0} f(j) where f(j)=[(-1)^(j+1)]*x^(2^(j+1)-2-j)/[(1-x)(1-x^3)(1-x^7)...(1-x^(2^j-1))].
1, 7, 9, 4, 1, 4, 7, 1, 8, 7, 5, 4, 1, 6, 8, 5, 4, 6, 3, 4, 9, 8, 4, 6, 4, 9, 8, 8, 0, 9, 3, 8, 0, 7, 7, 6, 3, 7, 0, 1, 3, 6, 4, 4, 1, 8, 2, 6, 5, 1, 3, 5, 5, 6, 4, 7, 1, 4, 1, 2, 9, 1, 4, 5, 8, 8, 1, 1, 0, 1, 1, 5, 3, 4, 1, 6, 7, 4, 3, 5, 8, 7, 9, 1, 1, 5, 2, 7, 5, 8, 7, 5, 7, 2, 8, 2, 5, 1, 5, 5
Offset: 1
Links
- S. R. Finch, Kalmar's composition constant, June 5, 2003. [Cached copy, with permission of the author]
- Philippe Flajolet and Helmut Prodinger, Level number sequences for trees.
Programs
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Mathematica
digits = 103; m0 = 5; dm = 2; Clear[f, g]; f[x_, m_] := Sum[((-1)^(j + 1)*x^( 2^(j + 1) - 2 - j))/Product[1 - x^(2^k - 1), {k, 1, j}] , {j, 1, m}] // N[#, digits]&; g[m_] := g[m] = (1/x /. FindRoot[f[x, m] == 1, {x, 5/9, 4/9, 6/9}, WorkingPrecision -> digits ]); g[m0]; g[m = m0 + dm]; While[RealDigits[g[m], 10, digits] != RealDigits[g[m - dm], 10, digits], Print["m = ", m]; m = m + dm]; RealDigits[g[m], 10, digits] // First (* Jean-François Alcover, Jun 19 2014 *)
Formula
1.79414718754168546349846498809380776370136441826513556471412914588110115...