A373097 a(n) = a[n/r] + a[n/r^2] + a[n/r^3] + ... , where a(0) = 0, a(1) = 1, r = 3/2, and [ ] = floor.

0, 1, 1, 2, 3, 4, 6, 7, 9, 12, 12, 14, 18, 18, 24, 24, 26, 29, 36, 36, 36, 48, 48, 49, 52, 54, 59, 72, 72, 72, 72, 78, 96, 96, 96, 98, 104, 104, 109, 118, 118, 144, 144, 144, 144, 144, 150, 156, 192, 192, 192, 192, 194, 196, 208, 208, 210, 218, 222, 236, 236

Offset: 0

Author

Clark Kimberling, Jul 22 2024

Keywords

• nonn

Comments

Conjecture: Let d(n) = a(n+1) - a(n) for n >= 0. Then d(n) = 1 for infinitely many n, and (d(n)) is unbounded.

Crossrefs

Cf. A000045, A373095, A373096.

Programs

Mathematica

a[0] = 0; a[1] = 1;
a[n_] := a[n] = Sum[a[Floor[n/(3/2)^k]], {k, 1, n}]
Table[a[n], {n, 0, 400}]