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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A119608 Let b(1)=0, b(2)= 1. b(2^m +k) = (b(2^m+1-k) + b(k))/2, 1 <= k <= 2^m, m >= 0. a(n) is numerator of b(n). 2
0, 1, 1, 1, 1, 3, 3, 1, 1, 7, 5, 3, 3, 5, 7, 1, 1, 15, 9, 7, 5, 11, 13, 3, 3, 13, 11, 5, 7, 9, 15, 1, 1, 31, 17, 15, 9, 23, 25, 7, 5, 27, 21, 11, 13, 19, 29, 3, 3, 29, 19, 13, 11, 21, 27, 5, 7, 25, 23, 9, 15, 17, 31, 1, 1, 63, 33, 31, 17, 47, 49, 15, 9, 55, 41, 23, 25, 39, 57, 7, 5, 59, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Denominator of b(n), for n >= 2, is A053644(n-1).

LINKS

Table of n, a(n) for n=1..83.

FORMULA

From Yosu Yurramendi, Mar 13 2019: (Start)

Without a(1) = 0, and shifting the terms one place left:

a(2^m) = 1, m >= 0;

a(2^(m+1)-1-k) = a(2^m+k), m >= 0, 0 < k < 2^m;

a(2^(m+1)+k) = a(2^m+k)+2^(m-floor(log2(k)))*a(k), m >= 0, 0 < k < 2^m.

(End)

MAPLE

A119608 := proc (mmax) local a, b, m, k, bn, i; b := [0, 1] ; for m from 1 to mmax do for k from 1 to 2^m do bn := (b[2^m+1-k]+b[k])/2 ; b := [op(b), bn] ; od ; od ; a := [] ; for i from 1 to nops(b) do a := [op(a), numer(b[i])] ; od ; RETURN(a) ; end: an := A119608(7) : for i from 1 to nops(an) do printf("%d, ", an[i]) ; od ; # R. J. Mathar, Aug 06 2006

PROG

(R)

maxlevel <- 8 # by choice

b <- c(0, 1)

for(m in 1:maxlevel) for(k in 1:2^m) b[2^m +k] = (b[2^m+1-k] + b[k])/2

d <- vector()

for(m in 0:maxlevel) for(k in 0:(2^m-1)) d[2^m + k] <- 2^m; d <- c(0, d)

a <- b*d

a[1:100]

# Yosu Yurramendi, Feb 05 2019

(R)

a <- 1

maxlevel <- 15 # by choice

for(m in 1:5) {

  a[2^(m+1)-1] <- 1

  a[2^(m+1)  ] <- 1

  for(k in 1:(2^m-1)){

  a[2^(m+1)-1-k] <- a[2^m+k]

  a[2^(m+1)  +k] <- a[2^m+k]+2^(m-floor(log2(k)))*a[k]

}}

a <- c(0, a)

a[1:128]

# Yosu Yurramendi, Mar 13 2019

CROSSREFS

Cf. A053644.

Sequence in context: A026515 A075772 A142157 * A196646 A196601 A196578

Adjacent sequences:  A119605 A119606 A119607 * A119609 A119610 A119611

KEYWORD

easy,nonn,frac

AUTHOR

Leroy Quet, Jun 04 2006

EXTENSIONS

More terms from R. J. Mathar, Aug 06 2006

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 November 15 13:56 EST 2019. Contains 329149 sequences. (Running on oeis4.)