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

1,4

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

Formula

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

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

Prog

(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)));

Crossrefs

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

Sequence in context: A112309 A160006 A060682 * A280363 A217743 A238845

Adjacent sequences: A352894 A352895 A352896 * A352898 A352899 A352900

Keyword

nonn

Author

Antti Karttunen, Apr 08 2022

Status

approved