This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048707 Numerators of ratios converging to Thue-Morse constant. 6
0, 1, 6, 105, 27030, 1771476585, 7608434000728254870, 140350834813144189858090274002849666665, 47758914269546354982683078068829456704164423862093743397580034411621752859030 (list; graph; refs; listen; history; text; internal format)



Also interpret each iteration of the construction of the Thue-Morse constant as a binary number converted to a decimal number. Thus (0_b, 01_b, 0110_b, 01101001_b ...) gives the present sequence in decimal. - Robert G. Wilson v, Sep 22 2006

a(n) corresponds to the binary value of the truth-table for the xor operator with n-arguments. - Joe Riel (joer(AT)san.rr.com), Jan 31 2010


Ariel S Koiman, Table of n, a(n) for n = 0..14

Beeler, M., Gosper, R. W. and Schroeppel, R., HAKMEM, ITEM 122 (Schroeppel, Gosper)

Eric Weisstein's World of Mathematics, Thue-Morse Sequence


a(0) = 0, a(n) = (a(n-1)+1)*((2^(2^(n-1)))-1).


Table[ FromDigits[ Nest[ Flatten[ #1 /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, n], 2], {n, 0, 8}] (* Robert G. Wilson v, Sep 22 2006 *)



; returns all but the last element of a list

(define rdc(lambda(x)(if(null? (cdr x))'()(cons (car x) (rdc (cdr x))))))

; gets the two's complement of a given bit

(define twosComplement (lambda (x)(if (eq? x #\0) "1" "0" )))

; gets the two's complement of a string

(define complementOfCurrent (lambda (x y z)(if (eq? (string-length y) z) y (complementOfCurrent (list->string (cdr (string->list x))) (string-append y (twosComplement (string-ref x 0))) z))))

; concatenates the two's complement of a string onto the current string, giving the next element in the TM sequence

(define concatenateComplement (lambda (x i)(if(zero? i) x (concatenateComplement(string-append x (complementOfCurrent x "" (string-length x)))(- i 1)))))

; generates the TM sequence of length 2^x

(define generateThue (lambda (x)(concatenateComplement "0" x)))

; if a bit is 1, get 2^i, where i is the index of that bit from right-left

(define F (lambda (c i)(if (eq? c #\1) (expt 2 i) 0)))

; gathers the sum of 2^index for all indices corresponding to a 1

(define fn (lambda (x sum i stop)(if (eq? i stop) sum (fn (list->string (rdc (string->list x))) (+ sum (F (string-ref x (-(string-length x) 1)) i)) (+ i 1)stop))))

(define f (lambda (x)(fn (generateThue x) 0 0 (string-length (generateThue x)))))

; format: (f x)

; example: (f 10)

; by Ariel S Koiman, Apr 23 2013


The denominators are given by A001146. Consists of every 2^n-th term of A019300. Cf. A048708 (same sequence in hexadecimal) and A014571, A010060, A014572.

Cf. A080814, A080815, A133468.

Sequence in context: A013300 A109819 A162130 * A259156 A075068 A055763

Adjacent sequences:  A048704 A048705 A048706 * A048708 A048709 A048710




Antti Karttunen, Mar 09 1999



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

Content is available under The OEIS End-User License Agreement .

Last modified November 28 18:55 EST 2015. Contains 264599 sequences.