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

Author

Jonas Wallgren

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

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 *)

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

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

Formula

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