A352891 Number of iterations of map x -> A341515(x) needed to reach x < n when starting from x=n, or 0 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, 6, 1, 3, 1, 11, 1, 3, 1, 9, 1, 7, 1, 11, 1, 3, 1, 6, 1, 6, 1, 9, 1, 11, 1, 7, 1, 1, 1, 91, 1, 106, 1, 5, 1, 16, 1, 14, 1, 4, 1, 7, 1, 20, 1, 89, 1, 3, 1, 7, 1, 3, 1, 87, 1, 21, 1, 1, 1, 50, 1, 92, 1, 5, 1, 18, 1, 3, 1, 8, 1, 98, 1, 14, 1, 5, 1, 14, 1, 34, 1, 6, 1, 35, 1, 12, 1, 2, 1, 21, 1, 71, 1, 90, 1, 3

Offset: 1

Author

Antti Karttunen, Apr 08 2022

Keywords

• nonn

Comments

This is one possible analog for A102419 ("Dropping time" sequence) when computed for A341515. See also A352894.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• 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, A352890, A352894.

Cf. also A102419.

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));
A352891(n) = if(n<=2, 0, my(k=0,x=n); while(x>=n, x = A341515(x); k++); (k));

Formula

For n >= 1, a(2n+1) = 1.

For n >= 1, A352894(n) <= a(n) <= A352890(n).