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%I #7 Dec 15 2015 12:51:38
%S 1,3,6,7,4,6,1,3,7,9,3,5,3,3,2,9,2,6,9,0,2,1,3,0,0,5,2,8,2,3,7,5,4,0,
%T 8,0,4,3,4,5,9,4,5,5,1,2,8,4,8,9,9,5,3,0,8,3,7,2,0,4,7,8,1,1,2,5,6,7,
%U 4,0,4,6,8,0,2,1,0,7,3,8,6,8,3,6,3,9,2,4,7,1,7,6,6,7,7,1,9,8,5,1,0,6,6,5,7,1,2,6,3,8,2,0,9,1,4,3,0,0,9,3,2,6,2,8,0,9,3,8,9,8,7,7,0,2,2,9,6,1,1,0,1,6,8,2,1,7,2,4,9,9,0,2,2,3,8,2,5,9,3,4,1,8,1,6,5,5,4,5,9,5,0,0,8,5,3,6,4,1,9,1,0,5,7,2,4,4,3,2,9
%N Decimal expansion of constant z = Sum_{n>=1} {(4/3)^n} * (3/4)^n, where {x} is the fractional part of x.
%F z = Sum_{n>=1} (4^n mod 3^n) / 4^n = Sum_{n>=1} A064629(n) / 4^n.
%e z = 1.3674613793533292690213005282375408043459455128489\
%e 95308372047811256740468021073868363924717667719851\
%e 06657126382091430093262809389877022961101682172499\
%e 02238259341816554595008536419105724432961711520592\
%e 92511101423029805093364719414748469451590148076361\
%e 52981353989027739504422481304813339179550172220838\
%e 78986350689080620566812697277477621308107983782819\
%e 76274774500215875970544025343446657398435575812229\
%e 28979675592867430344641751297842513480112243120370\
%e 37616509374801184872891959991759744341259271254468...
%e INFINITE SERIES.
%e z = 1/4 + 7/4^2 + 10/4^3 + 13/4^4 + 52/4^5 + 451/4^6 + 1075/4^7 + 6487/4^8 + 6265/4^9 + 44743/4^10 + 119923/4^11 + 302545/4^12 + 147298/4^13 + 589192/4^14 + 11922706/4^15 + 33341917/4^16 + 4227505/4^17 + 146050183/4^18 + 584200732/4^19 + 1174541461/4^20 +...+ A064629(n)/4^n +...
%Y Cf. A064629 (4^n mod 3^n), A264918, A264919, A264920, A264922.
%K nonn,cons
%O 1,2
%A _Paul D. Hanna_, Dec 03 2015
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