A138890 Non-Padovan numbers.

6, 8, 10, 11, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 1

Author

Omar E. Pol, Apr 05 2008

Keywords

• easy
• nonn

Comments

Natural numbers that are not in the Padovan sequence A000931.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Chai Wah Wu, Algorithms for complementary sequences, arXiv:2409.05844 [math.NT], 2024.

Crossrefs

Cf. A000931, A001690, A062289, A092460, A134816, A138836, A138888, A138891.

Programs

Mathematica

Complement[Range[0, Max[#]], #] &@ Union@ LinearRecurrence[{0, 1, 1}, {1, 0, 0}, 23] (* Michael De Vlieger, Sep 17 2024 *)

Python

def A138890(n):
    def f(x):
        if x<=1: return n+1
        a, b, c, d = 1, 1, 1, 0
        while c<=x:
            a, b, c = b, c, a+b
            d += 1
        return n+d-1
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Sep 10 2024