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

0,3

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

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.

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

Crossrefs

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

Sequence in context: A331269 A073907 A131424 * A222249 A230565 A072797

Adjacent sequences: A336282 A336283 A336284 * A336286 A336287 A336288

Keyword

nonn,base,fini,look

Author

Rémy Sigrist, Jul 22 2020.

Extensions

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

Status

approved