A352890 Number of iterations of map x -> A341515(x) needed to reach x <= 2 when starting from x=n, or -1 if such number is never reached. Here A341515 is the Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).

0, 0, 1, 7, 2, 5, 3, 16, 8, 19, 4, 14, 5, 12, 6, 17, 6, 9, 7, 20, 20, 26, 8, 15, 9, 27, 17, 13, 9, 7, 10, 106, 13, 121, 7, 111, 11, 122, 27, 34, 12, 21, 13, 27, 15, 35, 14, 104, 10, 23, 28, 28, 15, 18, 21, 102, 122, 36, 16, 29, 17, 156, 21, 107, 14, 14, 18, 122, 123, 109, 19, 112, 20, 113, 10, 123, 8, 28, 21, 35

Offset: 1

Author

Antti Karttunen, Apr 08 2022

Keywords

• nonn
• look

Comments

The unbroken ray in the scatter plot corresponds to primes.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25005
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000040, A005940, A006577, A064989, A156552, A329603, A341515.

Cf. also A352891, A352892, A352893, A352894.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
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 };
A329603(n) = A005940(2+(3*A156552(n)));
A341515(n) = if(n%2, A064989(n), A329603(n));
A352890(n) = { my(k=0); while(n>2, n = A341515(n); k++); (k); };

Formula

If n <= 2, a(n) = 0, otherwise a(n) = 1 + a(A341515(n)).

For n > 1, a(n) = A006577(A156552(n)).

For n >= 1, a(A000040(n)) = n-1.

For n >= 1, a(n) >= A352891(n).

For n >= 1, a(n) >= A352893(n).