A375650 a(n) is the cardinality of the sumset of the Collatz trajectory of n.

1, 3, 23, 6, 18, 24, 69, 10, 71, 22, 68, 25, 41, 69, 125, 15, 61, 73, 104, 28, 36, 68, 110, 33, 115, 48, 3060, 69, 95, 131, 2951, 21, 133, 67, 92, 76, 108, 108, 297, 37, 3007, 45, 203, 76, 105, 117, 2914, 45, 147, 119, 183, 57, 70, 3081, 3060, 82, 228, 102, 284

Offset

1,2

Comments

"Sumset" of a set S = {s_i} means the set of sums of pairs, s_i + s_j with i <= j.

Links

Markus Sigg, Table of n, a(n) for n = 1..10000

Example

The Collatz trajectory of 3 is {3,10,5,16,8,4,2,1}, which has the sumset {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,24,26,32} of size 23, so a(3) = 23.

Prog

(PARI) a(n) = {
  my(T = List([n]), S = Set());
  while(n > 1, n = if(n % 2 == 0, n/2, 3*n+1); listput(T, n));
  for(i = 1, #T,
    for(j = i, #T,
      S = setunion(S, Set([T[i] + T[j]]));
    )
  );
  #S
};
print(vector(59, n, a(n)));
(Python)
def a(n):
    T, S = [n], set()
    while n > 1:
        if n & 1 == 0: n >>= 1
        else: n = 3 * n + 1
        T.append(n)
    for i in range(len(T)):
        for j in range(i, len(T)):
            S.add(T[i] + T[j])
    return len(S)
print([a(n) for n in range(1, 60)]) # Darío Clavijo, Aug 24 2024

Crossrefs

A375006 is the list of those n for which a(n) < A008908(n) * (A008908(n) + 1) / 2.

Sequence in context: A105433 A196086 A196083 * A285098 A088605 A272816

Adjacent sequences: A375647 A375648 A375649 * A375651 A375652 A375653

Keyword

nonn

Author

Markus Sigg, Aug 24 2024

Status

approved