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A062295 A B_2 sequence: a(n) is the smallest square such that pairwise sums of not necessarily distinct elements are all distinct.

%I A062295 #14 Feb 16 2025 08:32:44
%S A062295 1,4,9,16,25,36,64,81,100,169,256,289,441,484,576,625,841,1089,1296,
%T A062295 1444,1936,2025,2401,2601,3136,4225,4356,4624,5329,5476,5776,6084,
%U A062295 7569,9025,10201,11449,11664,12321,12996,13456,14400,16129,17956,20164,22201
%N A062295 A B_2 sequence: a(n) is the smallest square such that pairwise sums of not necessarily distinct elements are all distinct.
%H A062295 Klaus Brockhaus, <a href="/A062295/b062295.txt">Table of n, a(n) for n = 1..4944</a>
%H A062295 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/B2-Sequence.html">B2-Sequence</a>
%H A062295 <a href="/index/Br#B_2">Index entries for B_2 sequences</a>
%e A062295 36 is in the sequence since the pairwise sums of {1, 4, 9, 16, 25, 36} are all distinct: 2, 5, 8, 10, 13, 17, 18, 20, 25, 26, 29, 32, 34, 37, 40, 41, 45, 50, 52, 61, 72.
%e A062295 49 is not in the sequence since 1 + 49 = 25 + 25.
%o A062295 (Python)
%o A062295 from itertools import count, islice
%o A062295 def A062295_gen(): # generator of terms
%o A062295     aset1, aset2, alist = set(), set(), []
%o A062295     for k in (n**2 for n in count(1)):
%o A062295         bset2 = {k<<1}
%o A062295         if (k<<1) not in aset2:
%o A062295             for d in aset1:
%o A062295                 if (m:=d+k) in aset2:
%o A062295                     break
%o A062295                 bset2.add(m)
%o A062295             else:
%o A062295                 yield k
%o A062295                 alist.append(k)
%o A062295                 aset1.add(k)
%o A062295                 aset2 |= bset2
%o A062295 A062295_list = list(islice(A062295_gen(),30)) # _Chai Wah Wu_, Sep 05 2023
%Y A062295 Cf. A000290, A011185, A010672, A025582, A005282, A062292, A133743, A133744.
%K A062295 nonn
%O A062295 1,2
%A A062295 _Labos Elemer_, Jul 02 2001
%E A062295 Edited, corrected and extended by _Klaus Brockhaus_, Sep 24 2007