Search: id:A033485
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%I A033485
%S A033485 1,2,3,5,7,10,13,18,23,30,37,47,57,70,83,101,119,142,165,
%T A033485 195,225,262,299,346,393,450,507,577,647,730,813,914,1015,
%U A033485 1134,1253,1395,1537,1702,1867,2062,2257,2482,2707,2969
%N A033485 a(n) = a(n-1) + a([n/2]), a(1) = 1.
%C A033485 a(A036554(n)) is even, a(A003159(n)) is odd. - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Oct 23 2002
%C A033485 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
%C A033485 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
%H A033485 T. D. Noe, <a href="b033485.txt">Table of n, a(n) for n=1..1000</a>
%F A033485 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
%F A033485 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
%F A033485 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
%F A033485 Sum_{k=1..n} a(k) = (a(2n+1)-1)/2. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Mar 18 2004
%t A033485 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)
%o A033485 (PARI) a(n)=if(n<2,1,a(floor(n/2))+a(n-1))
%Y A033485 Cf. A040039. Also half of A000123 (with first term omitted).
%Y A033485 Cf. A022907.
%Y A033485 Sequence in context: A008766 A103232 A062684 this_sequence A026811 A001401 
               A008628
%Y A033485 Adjacent sequences: A033482 A033483 A033484 this_sequence A033486 A033487 
               A033488
%K A033485 nonn,nice,easy
%O A033485 1,2
%A A033485 DELEHAM Philippe [BP 29, Coconi, 97670 Ouangani, Mayotte] (kolotoko(AT)wanadoo.fr)

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