A352897 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).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Apr 08 2022

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for sequences computed from indices in prime factorization

Crossrefs

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

Programs

PARI

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

PARI

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

PARI

A139391(n) = my(x = if(n%2, 3*n+1, n/2)); x/2^valuation(x, 2); \\ From A139391
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 };
A333860(n) = { my(mw=1); while(n>1, mw = max(hammingweight(n),mw); n = A139391(n)); (mw); };
A352897(n) = if(1==n,0,A333860(A156552(n)));

Formula

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

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