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A264918 Decimal expansion of constant z = Sum_{n>=1} {(3/2)^n} / 2^n, where {x} denotes the fractional part of x. 5
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A305274 A293382 A016674 * A091670 A201416 A072560

Adjacent sequences:  A264915 A264916 A264917 * A264919 A264920 A264921

KEYWORD

nonn,cons

AUTHOR

Paul D. Hanna, Dec 03 2015

STATUS

approved

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Last modified May 19 22:32 EDT 2019. Contains 323411 sequences. (Running on oeis4.)