This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352896 #14 Apr 09 2022 14:59:31
%S A352896 0,1,1,2,1,1,1,3,2,3,1,3,1,3,2,4,1,2,1,4,3,4,1,4,2,3,3,4,1,1,1,8,3,8,
%T A352896 2,8,1,8,4,5,1,3,1,4,3,6,1,8,2,4,3,4,1,3,3,8,8,5,1,3,1,8,4,8,3,3,1,8,
%U A352896 8,8,1,8,1,8,3,8,2,4,1,6,4,7,1,4,4,7,6,5,1,3,3,6,5,8,3,8,1,3,4,4,1,3,1,8,3
%N A352896 Maximum value of bigomega (A001222) computed for the terms x after the initial n, when map x -> A352892(x) is iterated starting from x=n down to the first x <= 2, or -1 if such number is never reached. Here A352892 is the next odd term in the Collatz or 3x+1 map (A139391) conjugated by unary-binary-encoding (A156552).
%C A352896 Equally, maximum value of bigomega (A001222) computed for the terms x after the initial n, when map x -> A341515(x) is iterated starting from x=n.
%H A352896 Antti Karttunen, <a href="/A352896/b352896.txt">Table of n, a(n) for n = 1..16384</a>
%H A352896 Antti Karttunen, <a href="/A352896/a352896.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A352896 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H A352896 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A352896 a(n) = A352897(A341515(n)) = A352897(A352892(n)).
%F A352896 For n > 1, a(n) = A352895(A156552(n)).
%o A352896 (PARI) A352896(n) = if(n<=2,n-1, my(m=0); while(n>2, n = A352892(n); m = max(m,bigomega(n))); (m)); \\ Needs also code from A352892.
%o A352896 (PARI) A352896(n) = if(n<=2,n-1,my(m=0); while(n>2, n = A341515(n); m = max(m,bigomega(n))); (m)); \\ Slower, but equivalent.
%o A352896 (PARI)
%o A352896 \\ Faster:
%o A352896 A139391(n) = my(x = if(n%2, 3*n+1, n/2)); x/2^valuation(x, 2); \\ From A139391
%o A352896 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A352896 A352895(n) = { my(mw=1); while(n>1, n = A139391(n); mw = max(hammingweight(n),mw)); (mw); };
%o A352896 A352896(n) = if(1==n,0,A352895(A156552(n)));
%Y A352896 Cf. A000040, A001222, A005940, A064989, A156552, A329603, A341515, A352892, A352895, A352897, A352899.
%K A352896 nonn,look
%O A352896 1,4
%A A352896 _Antti Karttunen_, Apr 08 2022