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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.

%I A011185 #26 Feb 05 2023 09:18:23
%S A011185 1,2,3,5,8,13,21,30,39,53,74,95,128,152,182,212,258,316,374,413,476,
%T A011185 531,546,608,717,798,862,965,1060,1161,1307,1386,1435,1556,1722,1834,
%U A011185 1934,2058,2261,2497,2699,2874,3061,3197,3332,3629,3712,3868,4140,4447,4640
%N A011185 A B_2 sequence: a(n) = least value such that sequence increases and pairwise sums of distinct elements are all distinct.
%C A011185 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 A011185 Klaus Brockhaus and Dan Hoey, <a href="/A011185/b011185.txt">Table of n, a(n) for n = 1..2839</a>
%H A011185 <a href="/index/Br#B_2">Index entries for B_2 sequences.</a>
%F A011185 a(n) = A010672(n-1)+1.
%o A011185 (Python)
%o A011185 from itertools import islice
%o A011185 def agen(): # generator of terms
%o A011185     aset, sset, k = set(), set(), 0
%o A011185     while True:
%o A011185         k += 1
%o A011185         while any(k+an in sset for an in aset): k += 1
%o A011185         yield k; sset.update(k+an for an in aset); aset.add(k)
%o A011185 print(list(islice(agen(), 51))) # _Michael S. Branicky_, Feb 05 2023
%Y A011185 Cf. A010672.
%Y A011185 Cf. A033627, A003278, A026471, A066720, A075122, A075123, A133097.
%Y A011185 Cf. A036241, A349777.
%K A011185 nonn
%O A011185 1,2
%A A011185 _Dan Hoey_