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

%I A375650 #27 Aug 26 2024 11:43:33
%S A375650 1,3,23,6,18,24,69,10,71,22,68,25,41,69,125,15,61,73,104,28,36,68,110,
%T A375650 33,115,48,3060,69,95,131,2951,21,133,67,92,76,108,108,297,37,3007,45,
%U A375650 203,76,105,117,2914,45,147,119,183,57,70,3081,3060,82,228,102,284
%N A375650 a(n) is the cardinality of the sumset of the Collatz trajectory of n.
%C A375650 "Sumset" of a set S = {s_i} means the set of sums of pairs, s_i + s_j with i <= j.
%H A375650 Markus Sigg, <a href="/A375650/b375650.txt">Table of n, a(n) for n = 1..10000</a>
%e A375650 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 A375650 (PARI) a(n) = {
%o A375650   my(T = List([n]), S = Set());
%o A375650   while(n > 1, n = if(n % 2 == 0, n/2, 3*n+1); listput(T, n));
%o A375650   for(i = 1, #T,
%o A375650     for(j = i, #T,
%o A375650       S = setunion(S, Set([T[i] + T[j]]));
%o A375650     )
%o A375650   );
%o A375650   #S
%o A375650 };
%o A375650 print(vector(59, n, a(n)));
%o A375650 (Python)
%o A375650 def a(n):
%o A375650     T, S = [n], set()
%o A375650     while n > 1:
%o A375650         if n & 1 == 0: n >>= 1
%o A375650         else: n = 3 * n + 1
%o A375650         T.append(n)
%o A375650     for i in range(len(T)):
%o A375650         for j in range(i, len(T)):
%o A375650             S.add(T[i] + T[j])
%o A375650     return len(S)
%o A375650 print([a(n) for n in range(1, 60)]) # _Darío Clavijo_, Aug 24 2024
%Y A375650 A375006 is the list of those n for which a(n) < A008908(n) * (A008908(n) + 1) / 2.
%K A375650 nonn
%O A375650 1,2
%A A375650 _Markus Sigg_, Aug 24 2024