1,2

a(A036554(n)) is even, a(A003159(n)) is odd. - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 23 2002

Partial sums of the sequence a(1)=1, a(1), a(1), a(2), a(2), a(3), a(3), a(4), a(4), a(5), a(5), a(6), ... example : a(1) = 1, a(2) = 1+1= 2, a(3) = 1+1+1= 3, a(4) = 1+1+1+2= 5, a(5) = 1+1+1+2+2= 7, ... - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 02 2004

The number of odd numbers before the n-th even number in this sequence is A003156(n). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 27 2004

T. D. Noe, Table of n, a(n) for n=1..1000

Conjecture: lim n ->infinity a(2n)/a(n)*log(n)/n = c = 1.64.... and a(n)/A(n) is bounded where A(n)=1 if n is a power of 2, otherwise A(n)=sqrt(n)*product(k<log2(n), n/2^k/log(n/2^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003

G.f.: A(x) satisfies x + (1+x)*A(x^2) = (1-x)*A(x). a(n) modulo 2 = A035263(n) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 25 2004

G.f.:(1/2)*(((1-x)*Product_{n>=0}(1-x^(2^n)))^(-1)-1). a(n) modulo 4 = A007413(n). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 28 2004

Sum_{k=1..n} a(k) = (a(2n+1)-1)/2. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 18 2004

b[1]=1; b[n_] := b[n]=Sum[b[k], {k, 1, n/2}]; Table[b[n], {n, 3, 105, 2}] (Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 22 2001)

(PARI) a(n)=if(n<2, 1, a(floor(n/2))+a(n-1))

Cf. A040039. Also half of A000123 (with first term omitted).

Cf. A022907.

Sequence in context: A008766 A103232 A062684 this_sequence A026811 A001401 A008628

Adjacent sequences: A033482 A033483 A033484 this_sequence A033486 A033487 A033488

nonn,nice,easy

DELEHAM Philippe [BP 29, Coconi, 97670 Ouangani, Mayotte] (kolotoko(AT)wanadoo.fr)