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

1,2

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

Example

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.

Prog

(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

Crossrefs

Cf. A000290, A062295, A133744, A133745.

Sequence in context: A030288 A030154 A122541 * A235484 A028820 A122683

Adjacent sequences: A133740 A133741 A133742 * A133744 A133745 A133746

Keyword

nonn

Author

Klaus Brockhaus, Sep 24 2007

Status

approved