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A382750 If k appears, 9*k does not.

%I A382750 #58 May 26 2025 11:47:01
%S A382750 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,
%T A382750 29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,46,47,48,49,50,51,52,53,
%U A382750 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
%N A382750 If k appears, 9*k does not.
%C A382750 Integers k with val(k, 9) even, where val(k, 9) is the 9-adic valuation of k.
%C A382750 Natural density 9/10.
%C A382750 Differs from A168183: 81 for example is not in A168183 but in this sequence. - _R. J. Mathar_, May 26 2025
%H A382750 Jan Snellman, <a href="/A382750/b382750.txt">Table of n, a(n) for n = 1..9000</a>
%H A382750 Jan Snellman, <a href="https://arxiv.org/abs/2504.02795">Greedy Regular Convolutions</a>, arXiv:2504.02795 [math.NT], 2025.
%e A382750 18 = 9*2 is not a term because 2 is a term.
%e A382750 162 = 9*18 is a term since 18 is not a term.
%t A382750 Select[Range[100], Mod[IntegerExponent[#, 3], 4] < 2 &] (* _Amiram Eldar_, May 12 2025 *)
%o A382750 (SageMath)
%o A382750 [_ for _ in range(1,100+1) if (valuation(_,3) % 4) < 2 ]
%o A382750 (Python)
%o A382750 from sympy import integer_log
%o A382750 def A382750(n):
%o A382750     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))
%o A382750     m, k = n, f(n)
%o A382750     while m != k: m, k = k, f(k)
%o A382750     return m # _Chai Wah Wu_, May 24 2025
%Y A382750 Cf. A003159, A007417, A382744, A382745, A382746.
%K A382750 nonn,easy
%O A382750 1,2
%A A382750 _Jan Snellman_, May 09 2025