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

1,2

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A328558 A072862 A300303 * A238203 A068802 A254073

Adjacent sequences: A062292 A062293 A062294 * A062296 A062297 A062298

Keyword

nonn

Author

Labos Elemer, Jul 02 2001

Extensions

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

Status

approved