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%I #13 Dec 15 2015 12:51:10
%S 7,5,5,9,4,0,2,0,4,4,8,0,1,0,6,0,6,6,4,7,1,4,4,1,0,6,8,0,4,0,6,0,0,4,
%T 7,8,1,6,8,7,0,3,9,5,1,6,3,9,6,8,7,2,3,0,4,5,3,2,6,2,7,1,5,6,6,3,3,0,
%U 5,8,9,1,2,5,6,2,8,8,1,0,4,8,6,5,0,6,4,6,5,1,7,4,9,7,6,2,9,6,9,8,3,3,1,6,9,8,4,9,3,5,8,9,1,4,0,5,4,5,1,1,7,4,5,1,7,7,7,0,3,2,1,4,1,6,6,9,2,3,2,9,1,7,3,7,0,2,6,7,0,5,9,1,4,9,2,9,4,3,2,4,1,8
%N Decimal expansion of constant z = Sum_{n>=1} {(3/2)^n} * (2/3)^n, where {x} is the fractional part of x.
%F z = Sum_{n>=1} (3^n mod 2^n) / 3^n = Sum_{n>=1} A002380(n) / 3^n.
%e z = 0.75594020448010606647144106804060047816870395163968\
%e 72304532627156633058912562881048650646517497629698\
%e 33169849358914054511745177703214166923291737026705\
%e 91492943241880014319515193043639253737676423992852\
%e 25627848946162966420904437623290023301210538408167\
%e 32840100004038800021575413579911936230620097811725\
%e 74486975449203289931795206458185235457647073997267\
%e 67563061259503400805979249157888064546156321001516\
%e 17847448155223110095055233059421134812069600436905\
%e 60954415853832952945591153477408523323724465192975...
%e INFINITE SERIES.
%e z = 1/3 + 1/3^2 + 3/3^3 + 1/3^4 + 19/3^5 + 25/3^6 + 11/3^7 + 161/3^8 + 227/3^9 + 681/3^10 + 1019/3^11 + 3057/3^12 + 5075/3^13 + 15225/3^14 + 29291/3^15+ 55105/3^16 + 34243/3^17 + 233801/3^18 + 439259/3^19 + 269201/3^20 +...+ A002380(n)/3^n +...
%Y Cf. A002380 (3^n mod 2^n), A264918, A264920, A264921, A264922.
%K nonn,cons
%O 1,1
%A _Paul D. Hanna_, Dec 03 2015
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