This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365515 #23 Feb 16 2025 08:34:06 %S A365515 0,0,1,0,1,2,0,1,3,3,0,1,4,7,4,0,1,5,13,12,5,0,1,6,21,32,20,6,0,1,7, %T A365515 31,55,71,30,7,0,1,8,43,108,153,124,44,8,0,1,9,57,154,366,368,218,65, %U A365515 9,0,1,10,73,256,668,926,856,375,80,10,0,1,11,91,333,1153,2214,2286,1424,572,96,11 %N A365515 Table read by antidiagonals upward: the n-th row gives the lexicographically earliest infinite B_n sequence starting from 0. %C A365515 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. Analogous to A347570 except that here the B_n sequences start from a(1) = 0. %H A365515 Chai Wah Wu, <a href="/A365515/b365515.txt">Table of n, a(n) for n = 1..242</a> %H A365515 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/B2-Sequence.html">B2 Sequence</a>. %F A365515 a(n) = A347570(n)-1. %e A365515 Table begins: %e A365515 n\k | 1 2 3 4 5 6 7 8 9 %e A365515 ----+--------------------------------------------------- %e A365515 1 | 0, 1, 2, 3, 4, 5, 6, 7, 8, ... %e A365515 2 | 0, 1, 3, 7, 12, 20, 30, 44, 65, ... %e A365515 3 | 0, 1, 4, 13, 32, 71, 124, 218, 375, ... %e A365515 4 | 0, 1, 5, 21, 55, 153, 368, 856, 1424, ... %e A365515 5 | 0, 1, 6, 31, 108, 366, 926, 2286, 5733, ... %e A365515 6 | 0, 1, 7, 43, 154, 668, 2214, 6876, 16864, ... %e A365515 7 | 0, 1, 8, 57, 256, 1153, 4181, 14180, 47381, ... %e A365515 8 | 0, 1, 9, 73, 333, 1822, 8043, 28296, 102042, ... %e A365515 9 | 0, 1, 10, 91, 500, 3119, 13818, 59174, 211135, ... %o A365515 (Python) %o A365515 from itertools import count, islice, combinations_with_replacement %o A365515 def A365515_gen(): # generator of terms %o A365515 asets, alists, klist = [set()], [[]], [0] %o A365515 while True: %o A365515 for i in range(len(klist)-1,-1,-1): %o A365515 kstart, alist, aset = klist[i], alists[i], asets[i] %o A365515 for k in count(kstart): %o A365515 bset = set() %o A365515 for d in combinations_with_replacement(alist+[k],i): %o A365515 if (m:=sum(d)+k) in aset: %o A365515 break %o A365515 bset.add(m) %o A365515 else: %o A365515 yield k %o A365515 alists[i].append(k) %o A365515 klist[i] = k+1 %o A365515 asets[i].update(bset) %o A365515 break %o A365515 klist.append(0) %o A365515 asets.append(set()) %o A365515 alists.append([]) %o A365515 A365515_list = list(islice(A365515_gen(),30)) %Y A365515 Cf. A001477 (n=1), A025582 (n=2), A051912 (n=3), A365300 (n=4), A365301 (n=5), A365302 (n=6), A365303 (n=7), A365304 (n=8), A365305 (n=9), A002061 (k=4), A369817 (k=5), A369818 (k=6), A369819 (k=7), A347570. %K A365515 nonn,tabl %O A365515 1,6 %A A365515 _Chai Wah Wu_, Sep 07 2023