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A375961 2-adic valuation of 6*n + 2.

%I A375961 #30 Oct 01 2024 08:51:23
%S A375961 1,3,1,2,1,5,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,7,1,2,1,3,1,2,1,4,1,2,1,3,
%T A375961 1,2,1,5,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,6,1,2,1,3,1,2,1,4,1,2,1,3,1,2,
%U A375961 1,5,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,9,1
%N A375961 2-adic valuation of 6*n + 2.
%C A375961 6*i+2 is the first (3*x+1)/2 successor of 4*i+1, with i >= 0.
%C A375961 The first occurrence of odd t is before that of t-1.
%H A375961 Ruud H.G. van Tol, <a href="/A375961/b375961.txt">Table of n, a(n) for n = 0..10000</a>
%H A375961 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>.
%F A375961 a(n) = A007814(6*n + 2).
%F A375961 a(n) = A371093(n) + 1.
%F A375961 a(n) = A087229(n) - 1.
%F A375961 a(n) = k for n == A096773(k) (mod 2^k), k >= 1.
%F A375961 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - _Amiram Eldar_, Oct 01 2024
%e A375961 a(21) = A007814(6*21+2) = 7.
%t A375961 a[n_] := IntegerExponent[6*n + 2, 2]; Array[a, 100, 0] (* _Amiram Eldar_, Sep 04 2024 *)
%o A375961 (PARI) a(n) = valuation(6*n+2, 2);
%o A375961 (Python)
%o A375961 def A375961(n): return (~(3*n+1)&3*n).bit_length()+1 # _Chai Wah Wu_, Sep 27 2024
%Y A375961 Cf. A007814, A016933, A087229, A087230, A096773, A371093, A375782.
%K A375961 nonn,easy
%O A375961 0,2
%A A375961 _Ruud H.G. van Tol_, Sep 04 2024