OFFSET

1,3

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

EXAMPLE

Beginning with k=0, the bag is initially empty and 0 matches nothing in the bag, so the sequence is extended and 0 is added to the bag. Likewise, for k=1-9, none of these digits match anything in the bag, resulting in the sequence [0,1,2,3,4,5,6,7,8,9] and a bag that contains {0,1,2,3,4,5,6,7,8,9}.

With k=10, Both the 1 and the 0 in k are matched with the 1 and the 0 in the bag and cancel out. This leaves an empty string, so the sequence is not extended, and the bag now contains {2,3,4,5,6,7,8,9}.

With k=11, neither digit cancels out, since there are no ones in the bag, so the sequence is extended, [0,1,2,3,4,5,6,7,8,9,11], and the bag contains {1,1,2,3,4,5,6,7,8,9}.

PROG

(Python)

seq = []

bag = ""

for k in range(1000):

m = str(k)

for digit in m:

if digit in bag:

mndx = m.index(digit)

m = m[:mndx] + m[mndx+1:]

bndx = bag.index(digit)

bag = bag[:bndx] + bag[bndx+1:]

if m:

seq.append(int(m))

bag = bag + m

print(seq)

(PARI) { my (b=vector(base=10), n=0); for (k=0, 105, d = if (k, digits(k, base), [0]); t = []; for (i=1, #d, if (b[1+d[i]], b[1+d[i]]--, t=concat(t, d[i]); ); ); if (#t, print1 (fromdigits(t, base)", "); for (j=1, #t, b[1+t[j]]++))) } \\ Rémy Sigrist, Dec 15 2019

CROSSREFS

KEYWORD

nonn,easy,base

AUTHOR

J. Stauduhar, Dec 14 2019

STATUS

approved