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A025582 A B_2 sequence: a(n) = least value such that sequence increases and pairwise sums of elements are all distinct. 13
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) = 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 1-14.

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 * A247556 A029452 A034434

Adjacent sequences:  A025579 A025580 A025581 * A025583 A025584 A025585

KEYWORD

nonn,changed

AUTHOR

Dan Hoey

STATUS

approved

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Last modified February 6 20:58 EST 2016. Contains 268049 sequences.