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 A025582 A B_2 sequence: a(n) is the least value such that sequence increases and pairwise sums of elements are all distinct. 23
 0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, 122, 147, 181, 203, 251, 289, 360, 400, 474, 564, 592, 661, 774, 821, 915, 969, 1015, 1158, 1311, 1394, 1522, 1571, 1820, 1895, 2028, 2253, 2378, 2509, 2779, 2924, 3154, 3353, 3590, 3796, 3997, 4296, 4432, 4778, 4850 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is also the least value such that sequence increases and pairwise differences of distinct elements are all distinct. LINKS David W. Wilson, Table of n, a(n) for n = 1..1000 Alon Amit, What are some interesting proofs using transfinite induction?, Quora, Nov 15 2014. LiJun Zhang, Bing Li, and LeeTang Cheng, Constructions of QC LDPC codes based on integer sequences, Science China Information Sciences, June 2014, Volume 57, Issue 6, pp 1-14. Eric Weisstein's World of Mathematics, B2 Sequence. Index entries for B_2 sequences. EXAMPLE After 0, 1, a(3) cannot be 2 because 2+0 = 1+1, so a(3) = 3. PROG (Sage) def A025582_list(n): a = [0] psums = set([0]) while len(a) < n: a += [next(k for k in IntegerRange(a[-1]+1, infinity) if not any(i+k in psums for i in a+[k]))] psums.update(set(i+a[-1] for i in a)) return a[:n] print(A025582_list(20)) # D. S. McNeil, Feb 20 2011 (Python) from itertools import count, islice def A025582_gen(): # generator of terms aset1, aset2, alist = set(), set(), [] for k in count(0): bset2 = {k<<1} if (k<<1) not in aset2: for d in aset1: if (m:=d+k) in aset2: break bset2.add(m) else: yield k alist.append(k) aset1.add(k) aset2 |= bset2 A025582_list = list(islice(A025582_gen(), 20)) # Chai Wah Wu, Sep 01 2023 CROSSREFS Row 2 of A365515. See A011185 for more information. A010672 is a similar sequence, but there the pairwise sums of distinct elements are all distinct. Sequence in context: A173256 A330285 A002049 * A247556 A337656 A029452 Adjacent sequences: A025579 A025580 A025581 * A025583 A025584 A025585 KEYWORD nonn,changed AUTHOR Dan Hoey STATUS approved

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Last modified February 28 14:09 EST 2024. Contains 370400 sequences. (Running on oeis4.)