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A372449 a(n) = A000523(A372444(n)); One less than the length of binary expansion of the n-th iterate of 27 with A371094.

%I A372449 #7 May 04 2024 11:58:21
%S A372449 4,7,12,23,44,84,165,326,650,1297,2590,5177,10349,20695,41386,82766,
%T A372449 165527,331048,662093,1324181,2648358,5296712,10593418,21186832,
%U A372449 42373658,84747311,169494616,338989224,677978441,1355956875,2711913744,5423827481,10847654953,21695309901,43390619796,86781239588,173562479173,347124958346
%N A372449 a(n) = A000523(A372444(n)); One less than the length of binary expansion of the n-th iterate of 27 with A371094.
%H A372449 Antti Karttunen, <a href="/A372449/b372449.txt">Table of n, a(n) for n = 0..1001</a>
%F A372449 a(n) = A000523(A372444(n)).
%F A372449 a(0) = A372447(0) = 4, and for n > 0, a(n) = A372447(n) + 2*A372448(n-1).
%o A372449 (PARI)
%o A372449 A000265(n) = (n>>valuation(n,2));
%o A372449 A000523(n) = logint(n,2);
%o A372449 A372443(n) = { my(x=27); while(n, x=A000265(3*x+1); n--); (x); };
%o A372449 A371093(n) = valuation(1+3*n,2);
%o A372449 A372447(n) = A000523(A372443(n));
%o A372449 A372448(n) = if(!n,1,2*A372448(n-1)+A371093(A372443(n)));
%o A372449 A372449(n) = if(0==n,A372447(n),A372447(n)+2*A372448(n-1));
%Y A372449 Cf. A371093, A371094, A372443, A372444, A372447, A372448.
%Y A372449 Column 14 of A372354.
%K A372449 nonn
%O A372449 0,1
%A A372449 _Antti Karttunen_, May 04 2024