A382744 If k appears, 5*k does not.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84

Offset

1,2

Comments

Also: numbers with an even number of 5's in their prime factorization.

Natural density 5/6.

Links

Jan Snellman, Table of n, a(n) for n = 1..8333

Jan Snellman, Greedy Regular Convolutions, arXiv:2504.02795 [math.NT], 2025.

Chai Wah Wu, Algorithms for Complementary Sequences, Integers (2025) Vol. 25, Art. No. A95. See p. 24.

Formula

a(n) ~ (6/5)*n.

Example

5 is removed since 5 = 5*1, 10 is removed, 15 is removed, 20 is removed, but 25 remains.

Maple

select(t -> padic:-ordp(t, 5)::even, [$1..100]); # Robert Israel, Apr 04 2025

Mathematica

Select[Range[100], EvenQ[IntegerExponent[#, 5]] &] (* Amiram Eldar, Apr 04 2025 *)

Prog

(SageMath)
[_ for _ in range(1, 100) if (valuation(_, 5) % 2) == 0]
(Python)
def ok(n):
    c = 0
    while n and n%5 == 0: n //= 5; c += 1
    return c&1 == 0
print([k for k in range(1, 82) if ok(k)]) # Michael S. Branicky, Apr 04 2025
(Python)
from sympy import integer_log
def A382744(n):
    def f(x): return n+x-sum((k:=x//5**m)-k//5 for m in range(0, integer_log(x, 5)[0]+1, 2))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Apr 10 2025

Crossrefs

Cf. A003159, A007417, A382745, A382746.

Sequence in context: A039199 A172269 A115180 * A045774 A045681 A001961

Adjacent sequences: A382741 A382742 A382743 * A382745 A382746 A382747

Keyword

nonn

Author

Jan Snellman, Apr 04 2025

Status

approved