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A011185 A B_2 sequence: a(n) = least value such that sequence increases and pairwise sums of distinct elements are all distinct. 17

%I #26 Feb 05 2023 09:18:23

%S 1,2,3,5,8,13,21,30,39,53,74,95,128,152,182,212,258,316,374,413,476,

%T 531,546,608,717,798,862,965,1060,1161,1307,1386,1435,1556,1722,1834,

%U 1934,2058,2261,2497,2699,2874,3061,3197,3332,3629,3712,3868,4140,4447,4640

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

%C 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.]

%H Klaus Brockhaus and Dan Hoey, <a href="/A011185/b011185.txt">Table of n, a(n) for n = 1..2839</a>

%H <a href="/index/Br#B_2">Index entries for B_2 sequences.</a>

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

%o (Python)

%o from itertools import islice

%o def agen(): # generator of terms

%o aset, sset, k = set(), set(), 0

%o while True:

%o k += 1

%o while any(k+an in sset for an in aset): k += 1

%o yield k; sset.update(k+an for an in aset); aset.add(k)

%o print(list(islice(agen(), 51))) # _Michael S. Branicky_, Feb 05 2023

%Y Cf. A010672.

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

%Y Cf. A036241, A349777.

%K nonn

%O 1,2

%A _Dan Hoey_

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)