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 A010672 A B_2 sequence: a(n) = least value such that sequence increases and pairwise sums of distinct elements are all distinct. 9
 0, 1, 2, 4, 7, 12, 20, 29, 38, 52, 73, 94, 127, 151, 181, 211, 257, 315, 373, 412, 475, 530, 545, 607, 716, 797, 861, 964, 1059, 1160, 1306, 1385, 1434, 1555, 1721, 1833, 1933, 2057, 2260, 2496, 2698, 2873, 3060, 3196, 3331, 3628, 3711, 3867, 4139, 4446, 4639 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Daniel Mondot and Giovanni Resta, Table of n, a(n) for n = 0..10000 (first 7611 terms from D. Mondot) Index entries for B_2 sequences. FORMULA a(n) = A011185(n+1)-1. - Robert Israel, May 02 2016 MAPLE N:= 10^6: # to get all terms <= N A[0]:= 0: Delta:= {}: As:= {A[0]}: Cands:= {\$1..N}: for n from 1 while Cands <> {} do A[n]:= min(Cands); Cands:= Cands minus ({A[n]} union map(`+`, Delta, A[n])); Delta:= Delta union map(t ->A[n] - t, As); As:= As union {A[n]}; od: seq(A[i], i=0..n-1); # Robert Israel, May 02 2016 PROG (MATLAB) N = 3*10^8; % to get all terms < N Cands = ones(N, 1); Delta = []; A = []; n = 1; while nnz(Cands) > 0 A(n) = find(Cands, 1, 'first'); Cands(A(n)) = 0; Rem = Delta(Delta <= N - A(n)) + A(n); Cands(Rem) = 0; Delta = union(Delta, -A(1:n-1)+A(n)); if mod(n, 10)==0 fprintf('a(%d)=%d\n', n, A(n)); toc; end n = n + 1; end A - 1 % Robert Israel, May 02 2016 (Python) from itertools import count, islice def A010672_gen(): # generator of terms aset2, alist = set(), [] for k in count(0): 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) A010672_list = list(islice(A010672_gen(), 30)) # Chai Wah Wu, Sep 11 2023 CROSSREFS A025582 is a similar sequence, but there the pairwise sums of (not necessarily distinct) elements are all distinct. Cf. A011185. Sequence in context: A125892 A072642 A105856 * A122515 A193840 A036372 Adjacent sequences: A010669 A010670 A010671 * A010673 A010674 A010675 KEYWORD nonn AUTHOR Dan Hoey STATUS approved

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Last modified October 3 19:07 EDT 2023. Contains 365870 sequences. (Running on oeis4.)