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0, 0, 1, 3, 5, 8, 10, 15, 27, 28, 23, 28, 20, 30, 22, 40, 32, 45, 27, 62, 89, 62, 116, 167, 105, 118, 108, 51, 99, 151, 88, 137, 137, 265, 174, 195, 320, 321, 249, 283, 226, 281, 293, 394, 465, 369, 585, 565, 639, 404, 483, 221, 233, 428, 384, 370, 527, 431, 818
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internal format)
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OFFSET
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1,4
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COMMENTS
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A005282 is the sequence of smallest numbers such that the pairwise sums of not necessarily distinct elements are all distinct, whereas A011185 is the sequence of smallest numbers such that the pairwise sums of distinct elements are all distinct.
Sequence has negative terms; the first one is a(65) = -130.
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LINKS
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EXAMPLE
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PROG
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(Python)
from itertools import count, islice
from collections import deque
def A133097_gen(): # generator of terms
aset2, alist, bset2, blist, aqueue, bqueue = set(), [], set(), [], deque(), deque()
for k in count(1):
cset2 = {k<<1}
if (k<<1) not in aset2:
for a in alist:
if (m:=a+k) in aset2:
break
cset2.add(m)
else:
aqueue.append(k)
alist.append(k)
aset2.update(cset2)
cset2 = set()
for b in blist:
if (m:=b+k) in bset2:
break
cset2.add(m)
else:
bqueue.append(k)
blist.append(k)
bset2.update(cset2)
if len(aqueue) > 0 and len(bqueue) > 0:
yield aqueue.popleft()-bqueue.popleft()
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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