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A133604 Elements of A005282 that are also the sum of a pair of not necessarily distinct elements of A005282.

%I A133604 #8 Sep 11 2023 17:53:12
%S A133604 2,4,8,21,66,97,204,565,662,775,970,1821,2780,6374,8730,8942,10898,
%T A133604 24596,55307,67189,79047,84345,164868,231694,233570,234619,271511,
%U A133604 298414,433973,474668,475800,567408,829129,839728,889285,1394240
%N A133604 Elements of A005282 that are also the sum of a pair of not necessarily distinct elements of A005282.
%C A133604 A005282 is the sequence of smallest numbers such that the pairwise sums of not necessarily distinct elements are all distinct.
%C A133604 Conjecture: 2, 4 and 8 are the only terms n such that n = 2*A005282(k) for some k.
%H A133604 Klaus Brockhaus, <a href="/A133604/b133604.txt">Table of n, a(n) for n = 1..98</a>
%e A133604 A005282(3) = 4 + 4 = 8 = A005282(4), hence 8 is in the sequence.
%e A133604 A005282(10) = 81, A005282(12) = 123. 81 + 123 = 204 = A005282(15), hence 204 is in the sequence.
%o A133604 (Python)
%o A133604 from itertools import count, islice
%o A133604 def A133604_gen(): # generator of terms
%o A133604     aset2, alist = set(), []
%o A133604     for k in count(1):
%o A133604         bset2 = {r:=k<<1}
%o A133604         if r not in aset2:
%o A133604             for d in alist:
%o A133604                 if (m:=d+k) in aset2:
%o A133604                     break
%o A133604                 bset2.add(m)
%o A133604             else:
%o A133604                 if k in aset2:
%o A133604                     yield k
%o A133604                 alist.append(k)
%o A133604                 aset2.update(bset2)
%o A133604 A133604_list = list(islice(A133604_gen(),30)) # _Chai Wah Wu_, Sep 11 2023
%Y A133604 Cf. A005282, A011185, A133605.
%K A133604 nonn
%O A133604 1,1
%A A133604 _Klaus Brockhaus_, Sep 18 2007