A343754 a(n) = 0, and for any n > 0, a(n+1) = a(n) - A065363(n) + 1.

0, 0, 1, 1, 0, 2, 3, 3, 4, 4, 3, 3, 2, 0, 3, 5, 6, 8, 9, 9, 10, 10, 9, 11, 12, 12, 13, 13, 12, 12, 11, 9, 10, 10, 9, 9, 8, 6, 5, 3, 0, 4, 7, 9, 12, 14, 15, 17, 18, 18, 21, 23, 24, 26, 27, 27, 28, 28, 27, 29, 30, 30, 31, 31, 30, 30, 29, 27, 30, 32, 33, 35, 36

Offset: 0

Author

Rémy Sigrist, Apr 27 2021

Keywords

• nonn
• base

Comments

This sequence has connections with A296062 and the Takagi (or blancmange) curve:

- for any real number x,

- let s(x) = min(frac(x), 1-frac(x)) (this is the building block of the Takagi curve),

- let t(x) = min(1/3, s(x)),

- let f(x) = Sum_{k >= 0} t(x * 3^k) / 3^k,

- the scatterplot of the sequence in the range A003462(k)..A003462(k+1)

approaches the curve x -> f(x)*3^k for x in the range 0..1.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..9841
• Rémy Sigrist, Scatterplot of the sequence for n = 0..A003462(11)
• Rémy Sigrist, Representation of f in the range 0..1
• Rémy Sigrist, Successive approximations of f
• Wikipedia, Blancmange curve

Crossrefs

Cf. A005823, A065363, A174574, A296062.

Programs

PARI

s=0; for (n=1, 73, print1 (s", "); m=n; while (m>1, s-=d=centerlift(Mod(m, 3)); m=(m-d)\3))

Formula

a(n) = n - A174574(n).

a(n) >= 0 with equality iff n belongs to A003462.

a(n) <= n/2 with equality iff n belongs to A005823.