A219087 a(n) = floor((n + 1/2)^(4/3)).

0, 1, 3, 5, 7, 9, 12, 14, 17, 20, 22, 25, 29, 32, 35, 38, 42, 45, 48, 52, 56, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 112, 116, 121, 125, 130, 134, 139, 143, 148, 152, 157, 162, 167, 172, 176, 181, 186, 191, 196, 201, 206, 211, 216, 221, 227

Offset: 0

Author

Clark Kimberling, Jan 01 2013

Keywords

• nonn
• easy

Comments

a(n) is the number k such that {k^p} < 1/2 < {(k+1)^p}, where p = 3/4 and { } = fractional part. Equivalently, the jump sequence of f(x) = x^(3/4), in the sense that these are the nonnegative integers k for which round(k^p) < round((k+1)^p). For details and a guide to related sequences, see A219085.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A219085, A219086.

Programs

Mathematica

Table[Floor[(n + 1/2)^(4/3)], {n, 0, 100}]

Formula

a(n) = floor((n + 1/2)^(4/3)).