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A372448 a(n) is the 2-adic valuation of 1 + 3*{the n-th iterate of 27 with A371094}.

%I A372448 #7 May 04 2024 11:58:18
%S A372448 1,4,9,19,39,79,160,322,645,1292,2585,5171,10344,20689,41379,82759,
%T A372448 165520,331043,662087,1324175,2648352,5296705,10593412,21186825,
%U A372448 42373651,84747303,169494607,338989215,677978433,1355956867,2711913735,5423827471,10847654946,21695309894,43390619790,86781239584,173562479171,347124958343
%N A372448 a(n) is the 2-adic valuation of 1 + 3*{the n-th iterate of 27 with A371094}.
%H A372448 Antti Karttunen, <a href="/A372448/b372448.txt">Table of n, a(n) for n = 0..1001</a>
%F A372448 a(n) = A371093(A372444(n)).
%F A372448 a(0) = 1, and for n > 0, a(n) = 2*a(n-1) + A371093(A372443(n)).
%o A372448 (PARI)
%o A372448 A000265(n) = (n>>valuation(n,2));
%o A372448 A372443(n) = { my(x=27); while(n, x=A000265(3*x+1); n--); (x); };
%o A372448 A371093(n) = valuation(1+3*n,2);
%o A372448 A372448(n) = if(!n,1,2*A372448(n-1)+A371093(A372443(n)));
%Y A372448 Cf. A371093, A371094, A372443, A372444, A372447, A372449.
%K A372448 nonn
%O A372448 0,2
%A A372448 _Antti Karttunen_, May 04 2024