A352897 - OEIS

%I #9 Apr 09 2022 14:59:47

%S 0,1,1,2,1,2,1,3,2,3,1,3,1,3,2,4,1,3,1,4,3,4,1,4,2,3,3,4,1,3,1,8,3,8,

%T 2,8,1,8,4,5,1,3,1,4,3,6,1,8,2,4,3,4,1,4,3,8,8,5,1,4,1,8,4,8,3,3,1,8,

%U 8,8,1,8,1,8,3,8,2,4,1,6,4,7,1,4,4,7,6,5,1,4,3,6,5,8,3,8,1,3,4,4,1,3,1,8,3

%N Maximum value of bigomega (A001222) computed for all the terms x (including the starting term x=n), when map x -> A352892(x) is iterated 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 Equally, maximum value of bigomega (A001222) computed for all the terms x (including the starting term x=n), when map x -> A341515(x) is iterated starting from x=n.

%H Antti Karttunen, <a href="/A352897/b352897.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A352897/a352897.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = max(A001222(n), A352896(n)).

%F For n > 1, a(n) = A333860(A156552(n)).

%o (PARI) A352897(n) = { my(m=bigomega(n)); while(n>2, m = max(m,bigomega(n)); n = A352892(n)); (m); }; \\ Uses the code from A352892.

%o (PARI) A352897(n) = { my(m=bigomega(n)); while(n>2, m = max(m,bigomega(n)); n = A341515(n)); (m); }; \\ Slightly slower.

%o (PARI)

%o A139391(n) = my(x = if(n%2, 3*n+1, n/2)); x/2^valuation(x, 2); \\ From A139391

%o 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 A333860(n) = { my(mw=1); while(n>1, mw = max(hammingweight(n),mw); n = A139391(n)); (mw); };

%o A352897(n) = if(1==n,0,A333860(A156552(n)));

%Y Cf. A001222, A156552, A333860, A341515, A352892, A352896, A352898.

%K nonn

%O 1,4

%A _Antti Karttunen_, Apr 08 2022