login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (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, 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_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 A337656 A029452

Adjacent sequences:  A025579 A025580 A025581 * A025583 A025584 A025585

KEYWORD

nonn

AUTHOR

Dan Hoey

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 03:33 EST 2022. Contains 358353 sequences. (Running on oeis4.)