A264918 Decimal expansion of constant z = Sum_{n>=1} {(3/2)^n} / 2^n, where {x} denotes the fractional part of x.

3, 9, 3, 1, 8, 8, 4, 7, 7, 0, 4, 9, 6, 4, 4, 3, 2, 4, 4, 9, 7, 2, 5, 8, 2, 1, 3, 1, 3, 8, 9, 0, 3, 8, 8, 5, 8, 5, 4, 8, 3, 9, 1, 4, 0, 7, 8, 8, 6, 6, 2, 8, 6, 9, 5, 3, 9, 2, 9, 3, 2, 4, 7, 5, 7, 5, 7, 8, 7, 7, 5, 8, 3, 3, 8, 9, 7, 4, 9, 8, 6, 6, 8, 1, 0, 9, 7, 6, 6, 6, 2, 0, 6, 1, 0, 1, 8, 5, 8, 8, 8, 0, 1, 3, 3, 3, 0, 0, 8, 0, 5, 9, 3, 2, 2, 6, 3, 1, 5, 3, 2, 6, 8, 0, 9, 0, 4, 7, 5, 0, 4, 9, 4, 2, 6, 6, 6, 1, 2, 1, 1, 4, 2, 4, 3, 3, 4, 9, 8, 4, 4, 3, 5, 8, 4, 7, 7, 5, 8, 5, 0, 6, 5, 5, 9, 3, 3, 7, 2, 5, 0, 9, 1, 4, 3, 2, 8, 8, 7, 7, 0, 5, 4, 3, 2, 2, 3, 1, 4, 0, 7, 7, 1, 7, 1, 7, 5, 9, 5, 3, 3, 3, 7, 7, 6

Offset

1,1

Links

Paul D. Hanna, Table of n, a(n) for n = 1..500

Formula

z = Sum_{n>=1} (3^n mod 2^n) / 4^n = Sum_{n>=1} A002380(n) / 4^n.

3 - z = Sum_{n>=1} [(3/2)^n] / 2^n = Sum_{n>=1} A002379(n) / 2^n, where [x] denotes the integer floor function of x.

Example

z = 0.39318847704964432449725821313890388585483914078866\
28695392932475757877583389749866810976662061018588\
80133300805932263153268090475049426661211424334984\
43584775850655933725091432887705432231407717175953\
33776901692614854937460993931094741172922114373160\
19617637538747813543456758934332723336245738884968...
INFINITE SERIES.
(1) z = 1/4 + 1/4^2 + 3/4^3 + 1/4^4 + 19/4^5 + 25/4^6 + 11/4^8 + 161/4^9 + 227/4^10 + 681/4^11 + 1019/4^12 +...+ A002380(n)/4^n +...
(2) 3 - z = 1/2 + 2/2^2 + 3/2^3 + 5/2^4 + 7/2^5 + 11/2^6 + 17/2^7 + 25/2^8 + 38/2^9 + 57/2^10 + 86/2^11 + 129/2^12 + 194/2^13 + 291/2^14 +...+ A002379(n)/2^n +...
where
3 - z = 2.60681152295035567550274178686109611414516...

Crossrefs

Cf. A002379 ([(3/2)^n]), A002380 (3^n mod 2^n), A264919, A264920, A264921, A264922.

Sequence in context: A374242 A336501 A016674 * A091670 A375503 A201416

Adjacent sequences: A264915 A264916 A264917 * A264919 A264920 A264921

Keyword

nonn,cons

Author

Paul D. Hanna, Dec 03 2015

Status

approved