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

1,4

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

Formula

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

For n >= 1, A352894(n) <= a(n) <= A352890(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));
A352891(n) = if(n<=2, 0, my(k=0, x=n); while(x>=n, x = A341515(x); k++); (k));

Crossrefs

Cf. A000040, A005940, A006577, A064989, A156552, A329603, A352890, A352894.

Cf. also A102419.

Sequence in context: A253686 A290101 A102419 * A339387 A074193 A074453

Adjacent sequences: A352888 A352889 A352890 * A352892 A352893 A352894

Keyword

nonn

Author

Antti Karttunen, Apr 08 2022

Status

approved