A071996 a(1) = 0, a(2) = 1, a(n) = a(floor(n/3)) + a(n - floor(n/3)).

0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 7, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 16, 16, 17, 17, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 21, 22, 23, 24, 24, 24, 25, 26, 26, 27

Offset: 1

Author

Jim Nastos, Jun 17 2002

Keywords

• easy
• nonn

Comments

"Rauzy's sequence" with initial values 0, 1.

David Moews showed that a(n)/n converges to about 0.31244. - Jim Nastos, Jan 08 2003

Difference of consecutive terms is always 0 or 1

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..10000
• David Moews, Asymptotic behavior of Rauzy's sequence
• Jeffrey Shallit, Ten Problems I Can't Solve (1.1MB ps)

Crossrefs

Cf. A071991, A071995.

Programs

Mathematica

a[1]=0; a[2]=1; a[n_] := a[n]=a[Floor[n/3]]+a[n-Floor[n/3]]; Table[a[n], {n, 1, 75}]

PARI

n = 33; v = vector(n); v[1] = 'x; v[2] = 'y;
for(i = 3, n, v[i] = v[floor(i/3)] + v[i - floor(i/3)]);
apply(e -> polcoeff(e, 1, v[2]), v) \\ Gheorghe Coserea, Aug 22 2015

Extensions

Edited by Robert G. Wilson v, Jun 23 2002