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A347570 Table read by antidiagonals upward: the n-th row gives the lexicographically earliest infinite B_n sequence. 2
1, 1, 2, 1, 2, 3, 1, 2, 4, 4, 1, 2, 5, 8, 5, 1, 2, 6, 14, 13, 6, 1, 2, 7, 22, 33, 21, 7, 1, 2, 8, 32, 56, 72, 31, 8, 1, 2, 9, 44, 109, 154, 125, 45, 9, 1, 2, 10, 58, 155, 367, 369, 219, 66, 10, 1, 2, 11, 74, 257, 669, 927, 857, 376, 81, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A B_n sequence is a sequence such that all sums a(x_1) + a(x_2) + ... + a(x_n) are distinct for 1 <= x_1 <= x_2 <= ... <= x_n.
LINKS
Eric Weisstein's World of Mathematics, B2 Sequence.
EXAMPLE
Table begins:
n\k | 1 2 3 4 5 6 7 8
----+------------------------------------------
1 | 1, 2, 3, 4, 5, 6, 7, 8, ...
2 | 1, 2, 4, 8, 13, 21, 31, 45, ...
3 | 1, 2, 5, 14, 33, 72, 125, 219, ...
4 | 1, 2, 6, 22, 56, 154, 369, 857, ...
5 | 1, 2, 7, 32, 109, 367, 927, 2287, ...
6 | 1, 2, 8, 44, 155, 669, 2215, 6877, ...
7 | 1, 2, 9, 58, 257, 1154, 4182, 14181, ...
8 | 1, 2, 10, 74, 334, 1823, 8044, 28297, ...
PROG
(Python)
from itertools import count, islice, combinations_with_replacement
def A347570_gen(): # generator of terms
asets, alists, klist = [set()], [[]], [1]
while True:
for i in range(len(klist)-1, -1, -1):
kstart, alist, aset = klist[i], alists[i], asets[i]
for k in count(kstart):
bset = set()
for d in combinations_with_replacement(alist+[k], i):
if (m:=sum(d)+k) in aset:
break
bset.add(m)
else:
yield k
alists[i].append(k)
klist[i] = k+1
asets[i].update(bset)
break
klist.append(1)
asets.append(set())
alists.append([])
A347570_list = list(islice(A347570_gen(), 30)) # Chai Wah Wu, Sep 06 2023
CROSSREFS
Cf. A000027 (n=1), A005282 (n=2), A096772 (n=3), A014206 (k=4).
Sequence in context: A216274 A145111 A104795 * A116925 A309010 A308500
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Sep 06 2021
STATUS
approved

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Last modified February 20 20:29 EST 2024. Contains 370217 sequences. (Running on oeis4.)