%I #14 Jan 12 2021 09:08:10

%S 1,12,2,123,13,23,3,1234,124,134,234,14,24,34,4,12345,1235,1245,1345,

%T 2345,125,135,145,235,245,345,15,25,35,45,5,123456,12346,12356,12456,

%U 13456,23456,1236,1246,1256,1346,1356,1456,2346,2356,2456,3456,126,136,146,156,236,246,256,346,356,456,16,26,36,46,56,6

%N Subsets of positive integers arranged in canonical order.

%C The order is self-explanatory (or see the Kubo-Vakil paper).

%C Of course once we reach subsets containing 10 this way of representing subsets by concatenation is unsatisfactory. Still, the sequence serves as a pointer to the Kubo-Vakil paper.

%C Sort by largest element, then decreasing size, then lexicographically (see Kubo-Vakil paper). - _Michael S. Branicky_, Jan 12 2021

%H Michael S. Branicky, <a href="/A213059/b213059.txt">Table of n, a(n) for n = 1..10000</a>

%H T. Kubo and R. Vakil, <a href="http://dx.doi.org/10.1016/0012-365X(94)00303-Z">On Conway's recursive sequence</a>, Discr. Math. 152 (1996), 225-252. a(n) is the concatenation of their S(n).

%o (Python)

%o from itertools import chain, combinations as C

%o def powerset(s): # in decreasing size

%o return chain.from_iterable(C(s, r) for r in range(len(s), -1, -1))

%o def agen():

%o m = 1 # largest element

%o while True:

%o for p in powerset(range(1, m)): yield int("".join(map(str, p+(m,))))

%o m += 1

%o def aupton(terms):

%o alst, g = [], agen()

%o while len(alst) < terms: alst += [next(g)]

%o return alst

%o print(aupton(63)) # _Michael S. Branicky_, Jan 12 2021

%Y Cf. A030299.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jun 03 2012

%E a(25) corrected by _Michael S. Branicky_, Jan 12 2021