login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A084188 a(0)=1, a(n+1) = 2*a(n) + b(n+2), where b(n)=A004539(n) is the n-th bit in the binary expansion of sqrt(2). 4
1, 2, 5, 11, 22, 45, 90, 181, 362, 724, 1448, 2896, 5792, 11585, 23170, 46340, 92681, 185363, 370727, 741455, 1482910, 2965820, 5931641, 11863283, 23726566, 47453132, 94906265, 189812531, 379625062, 759250124 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numerators in approximation sqrt(2) ~ a(n)/2^n.

a(n) is the number k such that {log_2(k} < 1/2 < {log_2(k+1)}, where { } = fractional part.  Equivalently, the jump sequence of f(x) = log_2(x), in the sense that these are the positive integers k for which round(log_2(k)) < round(log_2(k+1)); see A219085. - Clark Kimberling, Jan 01 2013

Largest k such that k^2 <= 2^(2n + 1). - Irina Gerasimova, Jul 07 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = floor(sqrt(2)*2^n).

a(n) = A017910(2*n+1). - # Peter Luschny, Sep 20 2011

MAPLE

A084188 := n->floor(sqrt(2)*2^n); # Peter Luschny, Sep 20 2011

MATHEMATICA

Table[Floor[Sqrt[2] 2^n], {n, 0, 30}] (* Harvey P. Dale, Aug 15 2013 *)

PROG

(PARI) a(n)=floor(sqrt(2)<<n) \\ Charles R Greathouse IV, Sep 22 2011

(Haskell)

a084188 n = a084188_list !! n

a084188_list = scanl1 (\u v -> 2 * u + v) a004539_list

-- Reinhard Zumkeller, Dec 16 2013

(MAGMA) [Isqrt(2^(2*n+1)):n in[0..40]] // Jason Kimberley, Oct 25 2016

(PARI) {a(n) = sqrtint(2*4^n)}; /* Michael Somos, Oct 29 2016 */

CROSSREFS

Cf. A084185, A084186, A017910.

Sequence in context: A024493 A130781 A071015 * A266721 A044432 A033120

Adjacent sequences:  A084185 A084186 A084187 * A084189 A084190 A084191

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, May 18 2003

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 21 17:26 EDT 2017. Contains 290891 sequences.