A332453 Starting from sigma(n), number of tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached.

0, 2, 0, 5, 2, 2, 0, 5, 2, 6, 2, 5, 5, 2, 2, 39, 6, 11, 1, 1, 0, 6, 2, 5, 39, 1, 1, 5, 5, 6, 0, 39, 2, 41, 2, 33, 6, 5, 5, 4, 1, 2, 4, 1, 11, 6, 2, 39, 10, 4, 6, 7, 41, 5, 6, 5, 1, 4, 5, 1, 39, 2, 2, 15, 1, 6, 3, 39, 2, 6, 6, 43, 6, 10, 39, 3, 2, 1, 1, 4, 34, 39, 1, 5, 41, 8, 5, 4, 4, 5, 5, 1, 0, 6, 5, 39, 7, 45, 11, 7, 7, 41, 2, 12, 2

Offset: 1

Author

Antti Karttunen, Feb 16 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A006667, A332209, A332452, A332455.

Programs

PARI

A006667(n) = { my(t=0); while(n>1, if(n%2, t++; n=3*n+1, n>>=1)); (t); };
A332453(n) = A006667(sigma(n));

Formula

a(n) = A006667(A000203(n)).

a(n) = A332209(n) - A332452(n).