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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 Chai Wah Wu, Table of n, a(n) for n = 1..241 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 Adjacent sequences: A347567 A347568 A347569 * A347571 A347572 A347573 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.)