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A371093 a(n) is the 2-adic valuation of 3n+1.

%I A371093 #29 Oct 25 2024 10:10:36
%S A371093 0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,6,0,1,0,2,0,1,0,3,0,1,0,2,
%T A371093 0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,
%U A371093 0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,8,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2
%N A371093 a(n) is the 2-adic valuation of 3n+1.
%C A371093 When a(n) is applied to square array A257852 we obtain square array A004736, or in other words, a(n) applied to any odd number gives the index of the row where it is located in array A257852.
%C A371093 See further comments in A087230.
%C A371093 The asymptotic density of the occurrences of k = 0, 1, 2, ... is 1/2^(k+1). The asymptotic mean of this sequence is 1. - _Amiram Eldar_, May 28 2024
%H A371093 Antti Karttunen, <a href="/A371093/b371093.txt">Table of n, a(n) for n = 0..65537</a>
%F A371093 a(n) = A007814(A016777(n)).
%F A371093 For all n >= 0, A067745(1+n) = A016777(n) / 2^a(n).
%F A371093 G.f.: Sum_{k>=1} k*x^(-1/3 + (-2)^(k + 1)/3 + 2^k)/(1 - x^(2^(k + 1))). - _Miles Wilson_, Sep 30 2024
%t A371093 Table[IntegerExponent[3*n+1, 2], {n, 0, 105}] (* _James C. McMahon_, Apr 21 2024 *)
%o A371093 (PARI) A371093(n) = valuation(1+3*n,2);
%o A371093 (Python)
%o A371093 def A371093(n): return ((m:=3*n) & ~(m+1)).bit_length() # _Chai Wah Wu_, Apr 20 2024
%Y A371093 Bisections: A000004, A087230.
%Y A371093 Cf. A004736, A007814, A016777, A067745, A257852.
%Y A371093 Cf. also A371092.
%K A371093 nonn,easy
%O A371093 0,2
%A A371093 _Antti Karttunen_, Apr 19 2024