A011185 A B_2 sequence: a(n) = least value such that sequence increases and pairwise sums of distinct elements are all distinct.

1, 2, 3, 5, 8, 13, 21, 30, 39, 53, 74, 95, 128, 152, 182, 212, 258, 316, 374, 413, 476, 531, 546, 608, 717, 798, 862, 965, 1060, 1161, 1307, 1386, 1435, 1556, 1722, 1834, 1934, 2058, 2261, 2497, 2699, 2874, 3061, 3197, 3332, 3629, 3712, 3868, 4140, 4447, 4640

Offset

1,2

Comments

a(n) = least positive integer > a(n-1) and not equal to a(i)+a(j)-a(k) for distinct i and j with 1 <= i,j,k <= n-1. [Comment corrected by Jean-Paul Delahaye, Oct 02 2020.]

Links

Klaus Brockhaus and Dan Hoey, Table of n, a(n) for n = 1..2839

Index entries for B_2 sequences.

Formula

a(n) = A010672(n-1)+1.

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    aset, sset, k = set(), set(), 0
    while True:
        k += 1
        while any(k+an in sset for an in aset): k += 1
        yield k; sset.update(k+an for an in aset); aset.add(k)
print(list(islice(agen(), 51))) # Michael S. Branicky, Feb 05 2023

Crossrefs

Cf. A010672.

Cf. A033627, A003278, A026471, A066720, A075122, A075123, A133097.

Cf. A036241, A349777.

Sequence in context: A080787 A065124 A048817 * A240733 A283936 A278800

Adjacent sequences: A011182 A011183 A011184 * A011186 A011187 A011188

Keyword

nonn

Author

Dan Hoey

Status

approved