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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))].
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%I #12 Jun 03 2017 12:57:47

%S 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,

%T 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,

%U 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

%N 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))].

%H S. R. Finch, <a href="/A001055/a001055.pdf">Kalmar's composition constant</a>, June 5, 2003. [Cached copy, with permission of the author]

%H Philippe Flajolet and Helmut Prodinger, <a href="http://algo.inria.fr/flajolet/Publications/FlPr87.pdf">Level number sequences for trees.</a>

%F 1.79414718754168546349846498809380776370136441826513556471412914588110115...

%t 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 *)

%Y Cf. A243350, A243584.

%K cons,easy,nonn

%O 1,2

%A Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 05 2005