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

1,2

Links

Table of n, a(n) for n=1..189.

Formula

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

Example

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.

Sequence in context: A055102 A243976 A198457 * A098990 A336453 A162195

Adjacent sequences: A264918 A264919 A264920 * A264922 A264923 A264924

Keyword

nonn,cons

Author

Paul D. Hanna, Dec 03 2015

Status

approved