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 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)
 OFFSET 0,3 COMMENTS 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 LINKS 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 FORMULA a(0) = 0, a(n) = (a(n-1)+1)*((2^(2^(n-1)))-1). MATHEMATICA Table[ FromDigits[ Nest[ Flatten[ #1 /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, n], 2], {n, 0, 8}] (* Robert G. Wilson v, Sep 22 2006 *) PROG (Scheme) ; 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 CROSSREFS 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 * A075068 A055763 A213464 Adjacent sequences:  A048704 A048705 A048706 * A048708 A048709 A048710 KEYWORD nonn,frac AUTHOR Antti Karttunen, Mar 09 1999 STATUS approved

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