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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

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 November 16 23:51 EST 2018. Contains 317275 sequences. (Running on oeis4.)