OFFSET
1,2
COMMENTS
For any n > 0, a(n) is the least number whose Collatz compressed trajectory starts with a succession of tripling and halvings steps encoded in the binary representation of n (beyond the leading one).
Each term appears infinitely many times as for any n > 0 either a(2*n) or a(2*n + 1) equals a(n).
LINKS
FORMULA
a(2^k) = 2^k for any k >= 0.
a(2^(k+1) - 1) = 2^k - 1 for any k >= 1.
a(A081254(n)) = 1 for any n >= 1.
EXAMPLE
The first terms, alongside the binary representation of n and some initial terms of the Collatz compressed trajectory of a(n), are:
n a(n) bin(n) traj(a(n))
-- ---- ------ ---------------------
1 1 1 (...)
2 2 10 ( 2, ...)
3 1 11 ( 1, ...)
4 4 100 ( 4, 2, ...)
5 2 101 ( 2, 1, ...)
6 1 110 ( 1, 2, ...)
7 3 111 ( 3, 5, ...)
8 8 1000 ( 8, 4, 2, ...)
9 4 1001 ( 4, 2, 1, ...)
10 2 1010 ( 2, 1, 2, ...)
11 6 1011 ( 6, 3, 5, ...)
12 5 1100 ( 5, 8, 4, ...)
13 1 1101 ( 1, 2, 1, ...)
14 3 1110 ( 3, 5, 8, ...)
15 7 1111 ( 7, 11, 17, ...)
16 16 10000 (16, 8, 4, 2, ...)
17 8 10001 ( 8, 4, 2, 1, ...)
18 4 10010 ( 4, 2, 1, 2, ...)
19 12 10011 (12, 6, 3, 5, ...)
20 10 10100 (10, 5, 8, 4, ...)
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
AUTHOR
Rémy Sigrist, May 15 2018
STATUS
approved