A342383 a(0) = 0; for n > 0, a(n) is the least positive integer not occurring earlier such that both the digits in a(n) and the digits in a(n-1)+a(n) are all distinct.

0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 13, 12, 14, 15, 16, 18, 17, 19, 20, 21, 24, 23, 25, 26, 27, 29, 28, 30, 31, 32, 35, 34, 36, 37, 38, 40, 39, 41, 42, 43, 46, 45, 47, 48, 49, 53, 50, 52, 51, 54, 69, 56, 64, 59, 61, 62, 58, 65, 60, 63, 57, 67, 68, 70, 72, 71, 74, 73, 75, 78, 76, 80, 79, 81, 82, 83

Offset

0,3

Comments

The sequence is finite due to the finite number of positive integers with distinct digits, see A010784, although the exact number of terms is currently unknown.

Links

Table of n, a(n) for n=0..76.

Scott R. Shannon, Image of the first 60000 terms. The green line is a(n) = n.

Example

a(1) = 1 as 1 has one distinct digit and a(0)+1 = 0+1 = 1 which has one distinct digit 0.
a(6) = 7 as 7 has one distinct digit and a(5)+7 = 5+7 = 12 which has two distinct digits. Note that 6 is the first skipped number as a(5)+6 = 5+6 = 11 has 1 as a duplicate digit.
a(11) = 13 as 13 has two distinct digits and a(10)+13 = 10+13 = 23 which has two distinct digits. Note that 11 and 12 are skipped as 11 has 1 as a duplicate digit while a(10)+12 = 10+12 = 22 has 2 as a duplicate digit.

Mathematica

Block[{a = {0}, k, m = 10^4}, Do[k = 1; While[Nand[FreeQ[a, k], AllTrue[DigitCount[a[[-1]] + k], # < 2 &], AllTrue[DigitCount[k], # < 2 &]], If[k > m, Break[]]; k++]; If[k > m, Break[]]; AppendTo[a, k], {i, 76}]; a] (* Michael De Vlieger, Mar 11 2021 *)

Prog

(Python)
def agen():
  alst, aset = [0], {0}
  yield 0
  while True:
    an = 1
    while True:
      while an in aset: an += 1
      stran, t = str(an), str(alst[-1] + an)
      if len(stran) == len(set(stran)) and len(t) == len(set(t)):
        alst.append(an); aset.add(an); yield an; break
      an += 1
g = agen()
print([next(g) for n in range(77)]) # Michael S. Branicky, Mar 11 2021

Crossrefs

Cf. A336285, A342382, A010784, A043537, A043096, A276633, A002378.

Sequence in context: A082325 A069787 A371592 * A371593 A358733 A086431

Adjacent sequences: A342380 A342381 A342382 * A342384 A342385 A342386

Keyword

nonn,base,fini,look

Author

Scott R. Shannon, Mar 09 2021

Status

approved