A076897 a(1)=1, a(n)=n-a(floor(3n/4)).

1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 8, 8, 8, 9, 10, 10, 11, 12, 13, 13, 13, 14, 15, 15, 15, 15, 16, 17, 18, 18, 19, 19, 20, 21, 22, 23, 23, 23, 24, 24, 25, 25, 26, 27, 27, 27, 28, 28, 28, 29, 30, 31, 31, 32, 33, 33, 34, 34, 35, 35, 36, 37, 38, 38, 39, 40, 41, 41, 41, 41, 42, 43

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

Conjecture: a(n) is asymptotic to 4n/7; (a(n)-4n/7)/log(n) is bounded.

From Robert Israel, Apr 13 2017: (Start)

Conjecture is true: in fact if D(n) = a(n) - 4*n/7, D(n) = (3*n-4*m)/7-D(m) where m = floor(3*n/4), so |D(n)| <= 4/7 + |D(m)|. Thus D(n) <= 3/7 + 4/7 log_(4/3)(n).

G.f. g(x) satisfies g(x) = x/(1-x)^2-((1+x^(1/3)+x^(2/3)+x)*g(x^(4/3))+(1+w*x^(1/3)+w^2*x^(2/3)+x)*g(w*x^(4/3))+(1+w^2*x^(1/3)+w*x^(2/3)+x)*g(w^2*x^(4/3)))/3, where w is a cube root of unity. (End)

Maple

A[1]:= 1: for n from 2 to 1000 do A[n]:= n - A[floor(3*n/4)] od:
seq(A[i], i=1..1000); # Robert Israel, Apr 13 2017

Prog

(PARI) a(n) = if(n<2, n, n - a(3*n\4)); \\ Indranil Ghosh, Apr 14 2017

Crossrefs

Sequence in context: A004001 A086841 A076502 * A316434 A066997 A006165

Adjacent sequences: A076894 A076895 A076896 * A076898 A076899 A076900

Keyword

nonn

Author

Benoit Cloitre, Nov 26 2002

Status

approved