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A B_2 sequence: a(n) is the smallest cube such that the pairwise sums of {a(1)...a(n)} are all distinct.
2

%I #6 Sep 05 2023 18:52:37

%S 1,8,27,64,125,216,343,512,729,1000,1331,2197,2744,3375,4913,5832,

%T 6859,8000,9261,10648,12167,15625,17576,19683,21952,24389,27000,29791,

%U 35937,42875,50653,54872,59319,64000,68921,74088,79507,85184,91125,97336

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

%C A Mian-Chowla sequence consisting only of cubes.

%e 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.

%o (Python)

%o from itertools import count, islice

%o def A062292_gen(): # generator of terms

%o aset1, aset2, alist = set(), set(), []

%o for k in (n**3 for n in count(1)):

%o bset2 = {k<<1}

%o if (k<<1) not in aset2:

%o for d in aset1:

%o if (m:=d+k) in aset2:

%o break

%o bset2.add(m)

%o else:

%o yield k

%o alist.append(k)

%o aset1.add(k)

%o aset2.update(bset2)

%o A062292_list = list(islice(A062292_gen(),30)) # _Chai Wah Wu_, Sep 05 2023

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

%K nonn

%O 1,2

%A _Labos Elemer_, Jul 02 2001