A019300 First n elements of Thue-Morse sequence A010060 read as a binary number.

0, 1, 3, 6, 13, 26, 52, 105, 211, 422, 844, 1689, 3378, 6757, 13515, 27030, 54061, 108122, 216244, 432489, 864978, 1729957, 3459915, 6919830, 13839660, 27679321, 55358643, 110717286, 221434573, 442869146, 885738292, 1771476585, 3542953171

Offset

0,3

Links

Ariel S Koiman, Table of n, a(n) for n = 0..3322

Formula

a(0) = 0, a(n+1) = 2a(n) + A010060(n). - Ralf Stephan, Sep 16 2003

Mathematica

With[{tm=Nest[Flatten[#/.{0->{0, 1}, 1->{1, 0}}]&, {0}, 7]}, Table[ FromDigits[ Take[tm, n], 2], {n, 40}]] (* Harvey P. Dale, Mar 25 2015 *)

Prog

(Scheme)
(define rdc(lambda(x)(if(null? (cdr x))'()(cons (car x) (rdc (cdr 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 (substring thue 0 (+ x 1)) 0 0 (string-length (substring thue 0 (+ x 1))) )))
(define thue "0110100110010110") ; Feel free to add Thue-Morse sequence of whatever length here
; Ariel S Koiman, May 07 2013
(PARI) a(n)=sum(k=1, n, (hammingweight(k)%2)<<(n-k)) \\ Charles R Greathouse IV, May 08 2016
(PARI) first(n)=my(v=vector(n)); v[1]=1; for(k=2, n, v[k]=2*v[k-1]+hammingweight(k)%2); concat(0, v) \\ Charles R Greathouse IV, May 08 2016

Crossrefs

Cf. A010060, A048707, A320916 (bit reversal).

Sequence in context: A255125 A267367 A265385 * A072762 A081254 A125049

Adjacent sequences: A019297 A019298 A019299 * A019301 A019302 A019303

Keyword

nonn,easy

Author

Jonas Wallgren

Status

approved