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

1, 4, 9, 16, 25, 36, 64, 81, 100, 169, 256, 289, 441, 484, 576, 625, 841, 1089, 1296, 1444, 1936, 2025, 2401, 2601, 3136, 4225, 4356, 4624, 5329, 5476, 5776, 6084, 7569, 9025, 10201, 11449, 11664, 12321, 12996, 13456, 14400, 16129, 17956, 20164, 22201

Offset: 1

Author

Labos Elemer, Jul 02 2001

Keywords

• nonn

Examples

			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.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..4944
• Eric Weisstein's World of Mathematics, B2-Sequence
• Index entries for B_2 sequences

Crossrefs

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

Programs

Python

from itertools import count, islice
def A062295_gen(): # generator of terms
    aset1, aset2, alist = set(), set(), []
    for k in (n**2 for n in count(1)):
        bset2 = {k<<1}
        if (k<<1) not in aset2:
            for d in aset1:
                if (m:=d+k) in aset2:
                    break
                bset2.add(m)
            else:
                yield k
                alist.append(k)
                aset1.add(k)
                aset2 |= bset2
A062295_list = list(islice(A062295_gen(),30)) # Chai Wah Wu, Sep 05 2023

Extensions

Edited, corrected and extended by Klaus Brockhaus, Sep 24 2007