A010672 A B_2 sequence: a(n) = least value such that the sequence increases and pairwise sums of distinct terms are all distinct.

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

Offset

0,3

Links

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