A376045 Complement of A325112.

3, 6, 9, 12, 13, 15, 16, 18, 19, 21, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 45, 46, 48, 49, 51, 53, 54, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 75, 76, 78, 79, 81, 83, 84, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 102, 103, 105, 106, 108

Offset: 1

Author

N. J. A. Sloane, Sep 09 2024

Keywords

• nonn
• base

Comments

Numbers missing from A325112.

Equivalently, numbers whose decimal expansion has a subsequence which is divisible by 3.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A325112.

Programs

Python

from itertools import combinations
def A376045(n):
    def f(x):
        c, l = 0, len(str(x))
        for i in range(l):
            k = 10**i
            for j in (1,2,4,5,7,8):
                if j*k<=x:
                    c += 1
        for a in combinations((10**i for i in range(l)),2):
            for b in ((1, 1), (1, 4), (1, 7), (2, 2), (2, 5), (2, 8), (4, 1), (4, 4), (4, 7), (5, 2), (5, 5), (5, 8), (7, 1), (7, 4), (7, 7), (8, 2), (8, 5), (8, 8)):
                if a[0]*b[0]+a[1]*b[1] <= x:
                    c += 1
        return n+c
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Sep 10 2024