%I A114041
%S A114041 3,6,9,8,6,8,7,4,3,4,8,4,8,4,7,9,4,4,8,9,5,8,4,8,7,7,0,2,9,5,9,4,8,1,8,
%T A114041 7,4,3,2,7,8,7,2,0,9,7,9,6,5,6,8,5,8,7,3,7,5,5,8,7,2,2,6,6,0,4,5,3,4,5,
%U A114041 8,6,0,3,2,0,9,6,4,8,4,8,5,2,1,2,8,4,5,3,3,9,5,2,3,7,1,8,2
%N A114041 Decimal expansion of -x, the real root of the power series with semiprime 
               coefficients.
%C A114041 This is the semiprime analog of A088751 "decimal expansion of -x, the 
               real root of the equation 0 = 1 + Sum{k=1,infinity} prime(k) x^k. 
               The inverse of Backhouse's constant (A072508)." Consider also the 
               polynomial sequence of truncations of this semiprime series, i.e. 
               P_20 = 57*x^20 + 55*x^19 + 51*x^18 + 49*x^17 + 46*x^16 + 39*x^15 
               + 38*x^14 + 35*x^13 + 34*x^12 + 33*x^11 + 26*x^10 + 25*x^9 + 22*x^8 
               + 21*x^7 + 15*x^6 + 14*x^5 + 10*x^4 + 9*x^3 + 6*x^2 + 4*x + 1. Interestingly 
               P_3 = 9*x^3 + 6*x^2 + 4*x + 1 = (3*x + 1)(3*x^2 + x + 1) and P_4 
               = 10*x^4 + 9*x^3 + 6*x^2 + 4*x + 1 = (2*x + 1)(5*x^3 + 2*x^2 + 2*x 
               + 1). Yet P_5 through P_20 are irreducible over Z.
%F A114041 a(n) = digits of -x where x is the real root of 1 + 4x + 6x^2 + 9x^3 
               + 10x^4 + 14x^5 ... = SUM[from i = 1 to infinity]A001358(i)*x^i.
%e A114041 -0.36986874348484794489584877...
%t A114041 Mathematica computation by T. D. Noe (noe(AT)sspectra.com).
%Y A114041 Cf. A001358, A088751.
%Y A114041 Sequence in context: A049341 A137991 A021077 this_sequence A057083 A000748 
               A160178
%Y A114041 Adjacent sequences: A114038 A114039 A114040 this_sequence A114042 A114043 
               A114044
%K A114041 cons,nonn
%O A114041 1,1
%A A114041 Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 01 2006