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A362757 The number of integers in the set f^n({0}), where f is a variant of the Collatz function that replaces any element x in the argument set with both x/2 and 3*x+1. 1
1, 2, 3, 5, 7, 10, 15, 22, 33, 48, 72, 103, 153, 221, 326, 477, 705, 1036, 1526, 2243, 3310, 4872, 7179, 10582, 15620, 23039, 33995, 50151, 73999, 109170, 161092, 237629, 350590, 517254, 763167, 1126070, 1661607, 2451715, 3617809, 5338044, 7876246, 11621318, 17147409, 25300982, 37331656, 55082911, 81275003 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A301756 A170877 A003410 * A018133 A261081 A116975
KEYWORD
nonn
AUTHOR
Markus Sigg, May 02 2023
STATUS
approved

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Last modified May 27 17:52 EDT 2024. Contains 372880 sequences. (Running on oeis4.)