A336285 a(0) = 0; for n > 0, a(n) is the least positive integer not occurring earlier such that the digits in a(n-1)+a(n) are all distinct.

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

Offset: 0

Author

Rémy Sigrist, Jul 22 2020

Keywords

• nonn
• base
• fini
• look

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.

Examples

			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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Scott R. Shannon, Image of the first 1000000 terms. The green line is a(n) = n.

Crossrefs

Cf. A342383, A338466, A322845, A010784, A043537, A043096, A276633, A002378.

Programs

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()
print([next(g) for n in range(77)]) # Michael S. Branicky, Mar 11 2021

Extensions

a(0)=0 added by N. J. A. Sloane, Mar 14 2021