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

1,4

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

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).

Prog

(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); };

Crossrefs

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

Cf. also A352891, A352892, A352893, A352894.

Sequence in context: A344762 A093072 A366599 * A066903 A194886 A196764

Adjacent sequences: A352887 A352888 A352889 * A352891 A352892 A352893

Keyword

nonn,look

Author

Antti Karttunen, Apr 08 2022

Status

approved