OFFSET
0,2
COMMENTS
a(n) is the number of integers in set A(n), where A(0) = {0} and A(n+1) = {x/2 : x in A(n)} union {3x+1 : x in A(n)}.
Non-integer numbers do not have integer offsprings. Consequently, they can be dropped when calculating terms of the sequence.
Apparently the limit of a(n)/a(n-1) is approximately equal to 1.47551 (see plot of a(n-1)/a(n) ~= 0.677732). An explanation of this limit would be desirable. - Hugo Pfoertner, May 06 2023
LINKS
Markus Sigg, Table of n, a(n) for n = 0..70
Hugo Pfoertner, Plot of ratio a(n-1)/a(n), using Plot 2.
EXAMPLE
a(3) = 5 is the number of integers in the set {0, 1/4, 1/2, 1, 2, 5/2, 4, 13}.
PROG
(PARI)
a362757(maxn) = {
my(A = Set([0]));
print1(1);
for(n = 1, maxn,
A = setunion([t >> 1 | t <- A, bitnegimply(1, t)], [3*t+1 | t <- A]);
print1(", ", #A);
);
};
CROSSREFS
KEYWORD
nonn
AUTHOR
Markus Sigg, May 02 2023
STATUS
approved