

A025582


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


12



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

1,3


COMMENTS

a(n) = 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
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_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]


CROSSREFS

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


KEYWORD

nonn


AUTHOR

Dan Hoey (Hoey(AT)AIC.NRL.Navy.Mil)


STATUS

approved



