A062292 A B_2 sequence: a(n) is the smallest cube such that the pairwise sums of {a(1)...a(n)} are all distinct.

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 2197, 2744, 3375, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 35937, 42875, 50653, 54872, 59319, 64000, 68921, 74088, 79507, 85184, 91125, 97336

Offset

1,2

Comments

A Mian-Chowla sequence consisting only of cubes.

Links

Table of n, a(n) for n=1..40.

Example

During recursive construction of this set, for n=1-50, the cubes of 12,18,24,32,34,36,48 are left out to keep all sums of distinct cubes distinct from each other.

Prog

(Python)
from itertools import count, islice
def A062292_gen(): # generator of terms
    aset1, aset2, alist = set(), set(), []
    for k in (n**3 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.update(bset2)
A062292_list = list(islice(A062292_gen(), 30)) # Chai Wah Wu, Sep 05 2023

Crossrefs

Cf. A011185, A010672, A025582, A005282, A062294.

Sequence in context: A118880 A048390 A000578 * A030295 A052045 A014187

Adjacent sequences: A062289 A062290 A062291 * A062293 A062294 A062295

Keyword

nonn

Author

Labos Elemer, Jul 02 2001

Status

approved