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

1, 4, 9, 16, 25, 36, 49, 100, 144, 169, 225, 256, 361, 441, 484, 625, 729, 784, 1156, 1521, 1600, 1764, 2401, 2704, 3364, 4096, 4225, 4356, 4900, 5184, 5929, 6889, 7921, 8836, 9216, 9409, 10404, 11881, 13689, 13924, 14161, 18496, 19321, 20449, 21316

Offset: 1

Author

Klaus Brockhaus, Sep 24 2007

Keywords

• nonn

Examples

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

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..4948
• Eric Weisstein's World of Mathematics, B2-Sequence
• Index entries for B_2 sequences

Crossrefs

Cf. A000290, A062295, A133744, A133745.

Programs

Python

from itertools import count, islice
def A133743_gen(): # generator of terms
    aset2, alist = set(), []
    for k in map(lambda x:x**2, count(1)):
        bset2 = set()
        for a in alist:
            if (b:=a+k) in aset2:
                break
            bset2.add(b)
        else:
            yield k
            alist.append(k)
            aset2.update(bset2)
A133743_list = list(islice(A133743_gen(),30)) # Chai Wah Wu, Sep 11 2023