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A025582
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A B_2 sequence: a(n) = least value such that sequence increases and pairwise sums of elements are all distinct.
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12
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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
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OFFSET
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1,3
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COMMENTS
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a(n) = least value such that sequence increases and pairwise differences of distinct elements are all distinct.
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LINKS
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David W. Wilson, Table of n, a(n) for n = 1..1000
Index entries for B_2 sequences.
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EXAMPLE
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After 0, 1, a(3) cannot be 2 because 2+0 = 1+1, so a(3) = 3.
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PROG
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(Sage)
def A025582_build(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] # [D. S. McNeil, Feb 20 2011]
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CROSSREFS
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See A011185 for more information.
A010672 is a similar sequence, but there the pairwise sums of distinct elements are all distinct.
Sequence in context: A130050 A173256 A002049 * A029452 A034434 A226229
Adjacent sequences: A025579 A025580 A025581 * A025583 A025584 A025585
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KEYWORD
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nonn
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AUTHOR
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Dan Hoey (Hoey(AT)AIC.NRL.Navy.Mil)
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STATUS
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approved
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