A264919 Decimal expansion of constant z = Sum_{n>=1} {(3/2)^n} * (2/3)^n, where {x} is the fractional part of x.

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..162.

Formula

z = Sum_{n>=1} (3^n mod 2^n) / 3^n = Sum_{n>=1} A002380(n) / 3^n.

Example

z = 0.75594020448010606647144106804060047816870395163968\
72304532627156633058912562881048650646517497629698\
33169849358914054511745177703214166923291737026705\
91492943241880014319515193043639253737676423992852\
25627848946162966420904437623290023301210538408167\
32840100004038800021575413579911936230620097811725\
74486975449203289931795206458185235457647073997267\
67563061259503400805979249157888064546156321001516\
17847448155223110095055233059421134812069600436905\
60954415853832952945591153477408523323724465192975...
INFINITE SERIES.
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 +...

Crossrefs

Cf. A002380 (3^n mod 2^n), A264918, A264920, A264921, A264922.

Sequence in context: A247876 A011474 A171536 * A233822 A199462 A195847

Adjacent sequences: A264916 A264917 A264918 * A264920 A264921 A264922

Keyword

nonn,cons

Author

Paul D. Hanna, Dec 03 2015

Status

approved