

A336285


a(0) = 0; for n > 0, a(n) is the least positive integer not occurring earlier such that the digits in a(n1)+a(n) are all distinct.


6



0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 53, 50, 52, 51, 54, 55, 65, 58, 62, 61, 59, 64, 56, 67, 57, 63, 60, 66, 68, 69, 70, 72, 71, 74, 73, 75, 77
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OFFSET

0,3


COMMENTS

In other words, for any n > 0, a(n) + a(n+1) belongs to A010784.
The sequence is finite since there are only a finite number of positive integers with distinct digits, see A010784, although the exact number of terms is currently unknown.


LINKS



EXAMPLE

The first terms, alongside a(n) + a(n+1), are:
n a(n) a(n)+a(n+1)
  
0 0 1
1 1 3
2 2 5
3 3 7
4 4 9
5 5 12
6 7 13
7 6 14
8 8 17
9 9 19
10 10 21


PROG

(PARI) s=0; v=1; for (n=1, 67, print1 (v", "); s+=2^v; for (w=1, oo, if (!bittest(s, w) && #(d=digits(v+w))==#Set(d), v=w; break)))
(Python)
def agen():
alst, aset, min_unused = [0], {0}, 1
yield 0
while True:
an = min_unused
while True:
while an in aset: an += 1
t = str(alst[1] + an)
if len(t) == len(set(t)):
alst.append(an); aset.add(an); yield an
if an == min_unused: min_unused = min(set(range(max(aset)+2))aset)
break
an += 1
g = agen()


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



