login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282496 'Somos expansion' of Pi: Pi=a(0)*sqrt(a(1)*sqrt(a(2)*sqrt(a(3)*sqrt(...)))). a(n)=floor(x(n)), x(n)=x(n-1)^2/a(n-1)^2, x(0)=Pi. 1
3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 3, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

1<=a(n)<=3 for all n. Reasoning: for x>1 it follows that 1<x/floor(x)<2.

LINKS

Yuriy Sibirmovsky, Table of n, a(n) for n = 0..1999

FORMULA

Product_{k>=0} a(k)^(1/2^k) = Pi.

EXAMPLE

Integer part of Pi is 3. Integer part of Pi^2/9 is 1.

MATHEMATICA

$MaxExtraPrecision = 1000;

x00 = Pi;

x0 = x00;

Nm = 130;

j = 1;

Res = Table[1, {j, 1, Nm}];

While[j < Nm, Res[[j]] = Floor[x0]; x0 = N[(x0/ Res[[j]])^2, 20000];

  j++];

Res

CROSSREFS

Cf. A000796 (digits), A100044 (Pi^2/9), A001203 (continued fraction), A276459 (another nested radical expansion).

Sequence in context: A344759 A337820 A322127 * A253238 A249773 A030369

Adjacent sequences:  A282493 A282494 A282495 * A282497 A282498 A282499

KEYWORD

nonn

AUTHOR

Yuriy Sibirmovsky, Feb 16 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)