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Elements of A011185 that are also the sum of a pair of distinct elements of A011185.
2

%I #9 Sep 12 2023 02:04:49

%S 3,5,8,13,21,74,95,182,212,413,862,1060,1435,1934,4447,5323,7588,

%T 19934,23725,24970,29558,43344,45425,48622,55240,63835,91336,98178,

%U 177387,180356,206088,333837,400924,418503,429115,598604,776150,990510,993089

%N Elements of A011185 that are also the sum of a pair of distinct elements of A011185.

%C A011185 is the sequence of smallest numbers such that the pairwise sums of distinct elements are all distinct.

%H Klaus Brockhaus, <a href="/A133605/b133605.txt">Table of n, a(n) for n = 1..75</a>

%e A011185(1) = 1, A011185(2) = 2. 1 + 2 = 3 = A011185(3), hence 3 is in the sequence.

%e A011185(16) = 212, A011185(35) = 1722. 212 + 1722 = 1934 = A011185(37), hence 1934 is in the sequence.

%o (Python)

%o from itertools import count, islice

%o def A133605_gen(): # generator of terms

%o aset2, alist = set(), []

%o for k in count(1):

%o bset2 = set()

%o for a in alist:

%o if (b:=a+k) in aset2:

%o break

%o bset2.add(b)

%o else:

%o if k in aset2:

%o yield k

%o alist.append(k)

%o aset2.update(bset2)

%o A133605_list = list(islice(A133605_gen(),30)) # _Chai Wah Wu_, Sep 11 2023

%Y Cf. A011185, A005282, A133604.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Sep 18 2007