A264921 Decimal expansion of constant z = Sum_{n>=1} {(4/3)^n} * (3/4)^n, where {x} is the fractional part of x.

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, 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, 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

Offset: 1

Author

Paul D. Hanna, Dec 03 2015

Keywords

• nonn
• cons

Examples

			z = 1.3674613793533292690213005282375408043459455128489\
95308372047811256740468021073868363924717667719851\
06657126382091430093262809389877022961101682172499\
02238259341816554595008536419105724432961711520592\
92511101423029805093364719414748469451590148076361\
52981353989027739504422481304813339179550172220838\
78986350689080620566812697277477621308107983782819\
76274774500215875970544025343446657398435575812229\
28979675592867430344641751297842513480112243120370\
37616509374801184872891959991759744341259271254468...
INFINITE SERIES.
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 +...
		

Crossrefs

Cf. A064629 (4^n mod 3^n), A264918, A264919, A264920, A264922.

Formula

z = Sum_{n>=1} (4^n mod 3^n) / 4^n = Sum_{n>=1} A064629(n) / 4^n.