

A025582


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


16



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) 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, LeeTang Cheng, Constructions of QC LDPC codes based on integer sequences, Science China Information Sciences, June 2014, Volume 57, Issue 6, pp 114.
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


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: A173256 A330285 A002049 * A247556 A029452 A294422
Adjacent sequences: A025579 A025580 A025581 * A025583 A025584 A025585


KEYWORD

nonn


AUTHOR

Dan Hoey


STATUS

approved



