login
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).
6
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, 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, 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
OFFSET
1,4
COMMENTS
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.
FORMULA
a(n) = A352897(A341515(n)) = A352897(A352892(n)).
For n > 1, a(n) = A352895(A156552(n)).
PROG
(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.
(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.
(PARI)
\\ Faster:
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 };
A352895(n) = { my(mw=1); while(n>1, n = A139391(n); mw = max(hammingweight(n), mw)); (mw); };
A352896(n) = if(1==n, 0, A352895(A156552(n)));
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Apr 08 2022
STATUS
approved