Search: a062295 -id:a062295
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0, 0, 0, 0, 0, 0, 15, -19, -44, 0, 31, 33, 80, 43, 92, 0, 112, 305, 140, -77, 336, 261, 0, -103, -228, 129, 131, 268, 429, 292, -153, -805, -352, 189, 985, 2040, 1260, 440, -693, -468, 239, -2367, -1365, -285, 885, 596, 3531, 2608, 3360, 2752, -2196, 0, 2709, 4367, 4411, 2105
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OFFSET
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1,7
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COMMENTS
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A062295 is the sequence of smallest squares such that the pairwise sums of not necessarily distinct elements are all distinct, whereas A133743 is the sequence of smallest squares such that the pairwise sums of distinct elements are all distinct.
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LINKS
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EXAMPLE
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PROG
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(Python)
from collections import deque
from itertools import count, islice
def A133744_gen(): # generator of terms
aset2, alist, bset2, blist, aqueue, bqueue = set(), [], set(), [], deque(), deque()
for k in (n**2 for n 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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A133743
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a(n) is the smallest positive square such that pairwise sums of distinct elements are all distinct.
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+10
4
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1, 4, 9, 16, 25, 36, 49, 100, 144, 169, 225, 256, 361, 441, 484, 625, 729, 784, 1156, 1521, 1600, 1764, 2401, 2704, 3364, 4096, 4225, 4356, 4900, 5184, 5929, 6889, 7921, 8836, 9216, 9409, 10404, 11881, 13689, 13924, 14161, 18496, 19321, 20449, 21316
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graph;
refs;
listen;
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OFFSET
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1,2
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LINKS
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EXAMPLE
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49 is in the sequence since the pairwise sums of distinct elements of {1, 4, 9, 16, 25, 36, 49} are all distinct: 5, 10, 13, 17, 20, 25, 26, 29, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 74, 85.
64 is not in the sequence since 1 + 64 = 16 + 49.
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PROG
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(Python)
from itertools import count, islice
def A133743_gen(): # generator of terms
aset2, alist = set(), []
for k in map(lambda x:x**2, count(1)):
bset2 = set()
for a in alist:
if (b:=a+k) in aset2:
break
bset2.add(b)
else:
yield k
alist.append(k)
aset2.update(bset2)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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1, 2, 3, 4, 5, 6, 10, 16, 23, 52, 71, 137, 224, 260, 361, 668, 695, 699, 1518, 1775, 1776, 3285, 7030, 36261
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graph;
refs;
listen;
history;
text;
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OFFSET
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1,2
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COMMENTS
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Conjecture: sequence is infinite.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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