A381229 a(n) is the number of distinct positive integers that can be obtained by starting with n, and optionally applying the operations square root, floor, and ceiling, in any order.

1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 7, 7, 7, 7, 7, 7

Offset

1,2

Links

Table of n, a(n) for n=1..87.

Example

For n = 15, sqrt(15) = 3.872..., floor and ceiling give 3 and 4. Sqrt(3) = 1.732..., and floor and ceiling give 1 and 2. 4 gives nothing new. In all, we get a(15) = 5 different numbers: 15, 3, 4, 1, 2.

Prog

(PARI) f(n) = my(t); if(n<4, [1..n], t=sqrtint(n); if(issquare(n), concat(f(t), n), Set(concat([f(t), f(t+1), [n]]))));
a(n) = #f(n);

Crossrefs

Cf. A381226, A381227, A381228.

Sequence in context: A348182 A029133 A255402 * A230411 A358551 A358372

Adjacent sequences: A381226 A381227 A381228 * A381230 A381231 A381232

Keyword

nonn

Author

N. J. A. Sloane and Jinyuan Wang, Feb 25 2025

Status

approved