cp's OEIS Frontend

A382744 If k appears, 5*k does not.

%I A382744 #39 Apr 11 2025 03:33:33
%S A382744 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,
%T A382744 31,32,33,34,36,37,38,39,41,42,43,44,46,47,48,49,50,51,52,53,54,56,57,
%U A382744 58,59,61,62,63,64,66,67,68,69,71,72,73,74,75,76,77,78,79,81,82,83,84
%N A382744 If k appears, 5*k does not.
%C A382744 Also: numbers with an even number of 5's in their prime factorization.
%C A382744 Natural density 5/6.
%H A382744 Jan Snellman, <a href="/A382744/b382744.txt">Table of n, a(n) for n = 1..8333</a>
%H A382744 Jan Snellman, <a href="https://arxiv.org/abs/2504.02795">Greedy Regular Convolutions</a>, arXiv:2504.02795 [math.NT], 2025.
%F A382744 a(n) ~ (6/5)*n.
%e A382744 5 is removed since 5 = 5*1, 10 is removed, 15 is removed, 20 is removed, but 25 remains.
%p A382744 select(t -> padic:-ordp(t,5)::even, [$1..100]); # _Robert Israel_, Apr 04 2025
%t A382744 Select[Range[100], EvenQ[IntegerExponent[#, 5]] &] (* _Amiram Eldar_, Apr 04 2025 *)
%o A382744 (SageMath)
%o A382744 [_ for _ in range(1,100) if (valuation(_,5) % 2) == 0]
%o A382744 (Python)
%o A382744 def ok(n):
%o A382744     c = 0
%o A382744     while n and n%5 == 0: n //= 5; c += 1
%o A382744     return c&1 == 0
%o A382744 print([k for k in range(1, 82) if ok(k)]) # _Michael S. Branicky_, Apr 04 2025
%o A382744 (Python)
%o A382744 from sympy import integer_log
%o A382744 def A382744(n):
%o A382744     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))
%o A382744     m, k = n, f(n)
%o A382744     while m != k: m, k = k, f(k)
%o A382744     return m # _Chai Wah Wu_, Apr 10 2025
%Y A382744 Cf. A003159, A007417, A382745, A382746.
%K A382744 nonn
%O A382744 1,2
%A A382744 _Jan Snellman_, Apr 04 2025