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A133743 a(n) is the smallest positive square such that pairwise sums of distinct elements are all distinct.

%I A133743 #15 Feb 16 2025 08:33:06
%S A133743 1,4,9,16,25,36,49,100,144,169,225,256,361,441,484,625,729,784,1156,
%T A133743 1521,1600,1764,2401,2704,3364,4096,4225,4356,4900,5184,5929,6889,
%U A133743 7921,8836,9216,9409,10404,11881,13689,13924,14161,18496,19321,20449,21316
%N A133743 a(n) is the smallest positive square such that pairwise sums of distinct elements are all distinct.
%H A133743 Klaus Brockhaus, <a href="/A133743/b133743.txt">Table of n, a(n) for n = 1..4948</a>
%H A133743 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/B2-Sequence.html">B2-Sequence</a>
%H A133743 <a href="/index/Br#B_2">Index entries for B_2 sequences</a>
%e A133743 49 is in the sequence since the pairwise sums of distinct elements of {1, 4, 9, 16, 25, 36, 49} are all distinct: 5, 10, 13, 17, 20, 25, 26, 29, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 74, 85.
%e A133743 64 is not in the sequence since 1 + 64 = 16 + 49.
%o A133743 (Python)
%o A133743 from itertools import count, islice
%o A133743 def A133743_gen(): # generator of terms
%o A133743     aset2, alist = set(), []
%o A133743     for k in map(lambda x:x**2, count(1)):
%o A133743         bset2 = set()
%o A133743         for a in alist:
%o A133743             if (b:=a+k) in aset2:
%o A133743                 break
%o A133743             bset2.add(b)
%o A133743         else:
%o A133743             yield k
%o A133743             alist.append(k)
%o A133743             aset2.update(bset2)
%o A133743 A133743_list = list(islice(A133743_gen(),30)) # _Chai Wah Wu_, Sep 11 2023
%Y A133743 Cf. A000290, A062295, A133744, A133745.
%K A133743 nonn
%O A133743 1,2
%A A133743 _Klaus Brockhaus_, Sep 24 2007