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

Author

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

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A381226, A381227, A381228.

Programs

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);