A133743 - OEIS

%I #14 Sep 12 2023 02:05:00

%S 1,4,9,16,25,36,49,100,144,169,225,256,361,441,484,625,729,784,1156,

%T 1521,1600,1764,2401,2704,3364,4096,4225,4356,4900,5184,5929,6889,

%U 7921,8836,9216,9409,10404,11881,13689,13924,14161,18496,19321,20449,21316

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

%H Klaus Brockhaus, <a href="/A133743/b133743.txt">Table of n, a(n) for n = 1..4948</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/B2-Sequence.html">B2-Sequence</a>

%H <a href="/index/Br#B_2">Index entries for B_2 sequences</a>

%e 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 64 is not in the sequence since 1 + 64 = 16 + 49.

%o (Python)

%o from itertools import count, islice

%o def A133743_gen(): # generator of terms

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

%o     for k in map(lambda x:x**2, 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             yield k

%o             alist.append(k)

%o             aset2.update(bset2)

%o A133743_list = list(islice(A133743_gen(),30)) # _Chai Wah Wu_, Sep 11 2023

%Y Cf. A000290, A062295, A133744, A133745.

%K nonn

%O 1,2

%A _Klaus Brockhaus_, Sep 24 2007