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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A165199 a(0) = 0, and for n>=1, let b(n,m) be the m-th digit, reading left to right, of binary n. (b(n, 1) is the most significant binary digit, which is 1.) Then a(n) is such that b(a(n),1)=1; and if b(n,m)=b(n,m-1) then b(a(n),m) does not = b(a(n),m-1); and if b(n,m) does not = b(n,m-1) then b(a(n), m) = b(a(n),m-1), for all m where 2 <= m <= number binary digits in n. 5
0, 1, 3, 2, 6, 7, 4, 5, 13, 12, 15, 14, 9, 8, 11, 10, 26, 27, 24, 25, 30, 31, 28, 29, 18, 19, 16, 17, 22, 23, 20, 21, 53, 52, 55, 54, 49, 48, 51, 50, 61, 60, 63, 62, 57, 56, 59, 58, 37, 36, 39, 38, 33, 32, 35, 34, 45, 44, 47, 46, 41, 40, 43, 42, 106, 107, 104, 105, 110, 111, 108 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is a self-inverse permutation of the positive integers.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..1023

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

FORMULA

From Antti Karttunen, Jul 22 2014: (Start)

a(0) = 0, and for n >= 1, a(n) = 2*a(floor(n/2)) + A000035(n+A000523(n)).

As a composition of related permutations:

a(n) = A056539(A129594(n)) = A129594(A056539(n)).

a(n) = A245443(A193231(n)) = A193231(A245444(n)).

a(n) = A075158(A243353(n)-1) = A075158((A241909(1+A075157(n))) - 1).

(End)

a(n) = A258746(A054429(n)) = A054429(A258746(n)), n > 0. - Yosu Yurramendi, Mar 29 2017

EXAMPLE

12 in binary is 1100. Generating a(12): the leftmost binary digit is 1. In 1100, the 2nd digit from the left equals the first, so the second digit from the left of binary a(12) does not equal the first; so we have 10 as the two leftmost digits in binary a(12). The third digit from the left of binary 12 does not equal the second, so the third digit from the left of binary a(12) equals the second; therefore the leftmost 3 digits of a(12) in binary are 100. And finally, the rightmost digit of binary 12 equals the 3rd from the left, so the rightmost digit of binary a(12) does not equal the 3rd from the left of binary a(12). Therefore a(12) in binary is 1001. And a(12) is the decimal equivalent of this, which is 9.

PROG

(Scheme, with memoizing definec-macro)

(definec (A165199 n) (if (zero? n) n (+ (* 2 (A165199 (floor->exact (/ n 2)))) (A000035 (+ (A000523 n) n)))))

;; Antti Karttunen, Jul 22 2014

(R)

maxrow <- 8 # by choice

a <- 1

for(m in 0: maxrow) for(k in 0:(2^m-1)){

a[2^(m+1) +       k] = a[2^(m+1) - 1 - k] + 2^(m+1)

a[2^(m+1) + 2^m + k] = a[2^(m+1) - 1 - k] + 2^m

}

(a <- c(0, a))

# Yosu Yurramendi, Apr 04 2017

CROSSREFS

Cf. A000035, A000523, A075157, A075158, A241909, A243353, A245443, A245444.

{A001477, A129594, A165199, A056539} form a 4-group.

Sequence in context: A154446 A154442 A154445 * A268825 A245812 A268826

Adjacent sequences:  A165196 A165197 A165198 * A165200 A165201 A165202

KEYWORD

base,nonn,look

AUTHOR

Leroy Quet, Sep 07 2009

EXTENSIONS

Extended by Ray Chandler, Sep 10 2009

a(0) = 0 prepended by Antti Karttunen, Jul 22 2014

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 October 22 13:19 EDT 2019. Contains 328318 sequences. (Running on oeis4.)