

A025582


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


23



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



EXAMPLE

After 0, 1, a(3) cannot be 2 because 2+0 = 1+1, so a(3) = 3.


PROG

(Sage)
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]
(Python)
from itertools import count, islice
def A025582_gen(): # generator of terms
aset1, aset2, alist = set(), set(), []
for k in count(0):
bset2 = {k<<1}
if (k<<1) not in aset2:
for d in aset1:
if (m:=d+k) in aset2:
break
bset2.add(m)
else:
yield k
alist.append(k)
aset1.add(k)
aset2 = bset2


CROSSREFS

A010672 is a similar sequence, but there the pairwise sums of distinct elements are all distinct.


KEYWORD

nonn,changed


AUTHOR



STATUS

approved



