A096772 A B3-sequence: a(1) = 1; for n>1, a(n) = smallest number > a(n-1) such that the sums of any three terms are all distinct.

1, 2, 5, 14, 33, 72, 125, 219, 376, 573, 745, 1209, 1557, 2442, 3098, 4048, 5298, 6704, 7839, 10987, 12332, 15465, 19144, 24546, 28974, 34406, 37769, 45864, 50877, 61372, 68303, 77918, 88545, 101917, 122032, 131625, 148575, 171237, 197815, 201454

Offset: 1

Author

Rick L. Shepherd, Aug 15 2004

Keywords

• nonn

Comments

This is the B3-sequence analog of the Mian-Chowla B2-sequence (A005282): Let a(1)=1; then use the greedy algorithm to choose the smallest a(n) > a(n-1) such that all sums a(i) + a(j) + a(k) are distinct for 1 <= i <= j <= k <= n. The reciprocal sum of the sequence for the first forty terms is 1.837412....

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..176
• Eric Weisstein's World of Mathematics, B2-Sequence.
• Eric Weisstein's World of Mathematics, Mian-Chowla Sequence.

Crossrefs

Row 3 of A347570.

Cf. A005282 (Mian-Chowla B2-sequence). A051912.

Programs

Python

from itertools import count, islice
def A096772_gen(): # generator of terms
    aset1, aset2, aset3, alist = set(), set(), set(), []
    for k in count(1):
        bset2, bset3 = {k<<1}, {3*k}
        if 3*k not in aset3:
            for d in aset1:
                if (m:=d+(k<<1)) in aset3:
                    break
                bset2.add(d+k)
                bset3.add(m)
            else:
                for d in aset2:
                    if (m:=d+k) in aset3:
                        break
                    bset3.add(m)
                else:
                    yield k
                    alist.append(k)
                    aset1.add(k)
                    aset2 |= bset2
                    aset3 |= bset3
A096772_list = list(islice(A096772_gen(),30)) # Chai Wah Wu, Sep 05 2023

Formula

a(n) = A051912(n-1) + 1. - Peter Kagey, Oct 20 2021