A382750 If k appears, 9*k does not.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81

Offset: 1

Author

Jan Snellman, May 09 2025

Keywords

• nonn
• easy

Comments

Integers k with val(k, 9) even, where val(k, 9) is the 9-adic valuation of k.

Natural density 9/10.

Differs from A168183: 81 for example is not in A168183 but in this sequence. - R. J. Mathar, May 26 2025

Examples

			18 = 9*2 is not a term because 2 is a term.
162 = 9*18 is a term since 18 is not a term.
		

Links

• Jan Snellman, Table of n, a(n) for n = 1..9000
• Jan Snellman, Greedy Regular Convolutions, arXiv:2504.02795 [math.NT], 2025.

Crossrefs

Cf. A003159, A007417, A382744, A382745, A382746.

Programs

Mathematica

Select[Range[100], Mod[IntegerExponent[#, 3], 4] < 2 &] (* Amiram Eldar, May 12 2025 *)

Python

from sympy import integer_log
def A382750(n):
    def f(x): return n+x-sum((k:=x//9**m)-k//9 for m in range(0,integer_log(x,9)[0]+1,2))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, May 24 2025

SageMath

[ for  in range(1,100+1) if (valuation(_,3) % 4) < 2 ]