A185543 Numbers not of the form floor(k^(3/2)); complement of A000093.

3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 90

Offset: 1

Author

Clark Kimberling, Jan 30 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Chai Wah Wu, Algorithms for complementary sequences, arXiv:2409.05844 [math.NT], 2024.

Crossrefs

Cf. A000093.

Programs

Mathematica

f[n_]=Floor[n^(3/2)]
t1=Table[f[n],{n,1,80}];t1  (* A000093 *)
t2=Complement[Range[200], Table[f[n],{n,1,80}]];t2  (* A185543 *)

Python

def A185543(n):
    def f(x): return n-1+(a:=integer_nthroot((x+1)**2,3))[0]+(a[1]^1)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Sep 10 2024