A B_2 sequence: a(n) is the smallest square such that the pairwise sums of {a(1)...a(n)} not necessarily distinct elements are all distinct.

1, 4, 9, 16, 25, 49, 36, 64, 81, 100, 144, 169, 196, 256, 289, 441, 484, 576, 625, 784, 841, 1089, 1296, 1444, 1681, 1764, 1936, 2025, 2304, 2401, 2809, 2916, 3721, 4096, 2601, 3136, 4225, 4356, 4624, 5329, 6400, 6561, 7056, 8100, 8464, 8836, 9801, 121005476, 5776, 6084, 7569, 9025, 10201, 11449, 11664, 12321, 12996, 13456, 14400, 16129, 17956, 20164, 22201

K. Brockhaus, <a href="http://www.research.att.com/~njas/sequences/b062295.txt">Table of n, a(n) for n = 1..4944</a>

E. W. Weisstein, <a href="http://mathworld.wolfram.com/B2-Sequence.html">B2-Sequence</a>

<a href="http://www.research.att.com/~njas/sequences/Sindx_Br.html#B_2">Index entries for B_2 sequences</a>

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.

49 is not in the sequence since 1 + 49 = 25 + 25.

Cf. A000290, A011185, A010672, A025582, A005282, A062292, A133743, A133744.

nonn,new

nonn

Edited, corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 24 2007

nonn,new

nonn

Labos E. (labos(AT)ana1ana.sote.hu), Jul 02 2001

A B_2 sequence: a(n) is the smallest square such that the pairwise sums of {a(1)...a(n)} are all distinct.

1, 4, 9, 16, 25, 49, 81, 100, 144, 169, 196, 256, 441, 484, 625, 784, 841, 1089, 1444, 1681, 1764, 2025, 2304, 2401, 2809, 2916, 3721, 4096, 4225, 5329, 6400, 6561, 7056, 8100, 8464, 8836, 9801, 12100

1,2

A011185, A010672, A025582, A005282.

nonn

Labos E. (labos(AT)ana1.sote.hu), Jul 02 2001

approved