A332455 Starting from sigma(n)+1, number of tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached.

0, 0, 1, 0, 5, 2, 6, 0, 5, 6, 2, 5, 5, 7, 7, 0, 6, 1, 1, 9, 8, 6, 7, 5, 0, 9, 40, 10, 39, 42, 8, 0, 7, 41, 7, 4, 11, 5, 10, 33, 9, 43, 4, 1, 11, 42, 7, 39, 5, 38, 42, 7, 41, 34, 42, 34, 6, 33, 5, 16, 39, 43, 12, 0, 1, 42, 3, 15, 43, 42, 42, 7, 3, 10, 39, 3, 43, 16, 6, 14, 5, 15, 1, 17, 41, 8, 34, 4, 33, 46, 2, 16, 44, 42, 34, 39

Offset: 1

Author

Antti Karttunen, Feb 16 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• 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, A088580, A202274, A332453, A332454.

Cf. also A324294, A332459.

Programs

PARI

A006667(n) = { my(t=0); while(n>1, if(n%2, t++; n=3*n+1, n>>=1)); (t); };
A332455(n) = A006667(1+sigma(n));

Formula

a(n) = A006667(A088580(n)) = A006667(1+sigma(n)).

a(2^n) = 0 for all n >= 0. [Zero occurs at least also at a(25). See A202274]