A375650 - OEIS

%I #27 Aug 26 2024 11:43:33

%S 1,3,23,6,18,24,69,10,71,22,68,25,41,69,125,15,61,73,104,28,36,68,110,

%T 33,115,48,3060,69,95,131,2951,21,133,67,92,76,108,108,297,37,3007,45,

%U 203,76,105,117,2914,45,147,119,183,57,70,3081,3060,82,228,102,284

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

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

%H Markus Sigg, <a href="/A375650/b375650.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%o (PARI) a(n) = {

%o   my(T = List([n]), S = Set());

%o   while(n > 1, n = if(n % 2 == 0, n/2, 3*n+1); listput(T, n));

%o   for(i = 1, #T,

%o     for(j = i, #T,

%o       S = setunion(S, Set([T[i] + T[j]]));

%o     )

%o   );

%o   #S

%o };

%o print(vector(59, n, a(n)));

%o (Python)

%o def a(n):

%o     T, S = [n], set()

%o     while n > 1:

%o         if n & 1 == 0: n >>= 1

%o         else: n = 3 * n + 1

%o         T.append(n)

%o     for i in range(len(T)):

%o         for j in range(i, len(T)):

%o             S.add(T[i] + T[j])

%o     return len(S)

%o print([a(n) for n in range(1, 60)]) # _Darío Clavijo_, Aug 24 2024

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

%K nonn

%O 1,2

%A _Markus Sigg_, Aug 24 2024