A342367 a(1) = 1; for n > 1, a(n) is the least positive integer not occurring earlier that shares a digit but not a factor > 1 with a(n-1).

1, 10, 11, 12, 13, 3, 23, 2, 21, 16, 15, 14, 17, 7, 27, 20, 29, 9, 19, 18, 31, 30, 37, 32, 25, 22, 123, 26, 61, 6, 65, 36, 35, 33, 34, 39, 38, 43, 4, 41, 24, 47, 40, 49, 44, 45, 46, 63, 53, 5, 51, 50, 57, 52, 55, 54, 59, 56, 67, 60, 101, 70, 71, 72, 73, 74, 75, 58, 81, 8, 83, 28, 85, 48

Offset: 1

Author

Scott R. Shannon, Mar 09 2021

Keywords

• nonn
• base

Comments

After 100000 terms the lowest unused number is 99986. It is almost certain that this sequence is a permutation of the positive integers.

Links

• Scott R. Shannon, Image of the first 1000 terms. The green line is a(n) = n.

Crossrefs

Cf. A342356 (share factor and digit), A342366 (share factor but not digit), A239664 (no shared factor or digit), A184992, A309151, A249591.

Programs

Mathematica

Block[{a = {1}, m = {1}, k}, Do[k = 2; While[Nand[FreeQ[a, k], GCD[k, a[[-1]]] == 1, IntersectingQ[m, IntegerDigits[k]]], k++]; AppendTo[a, k]; Set[m, IntegerDigits[k]], {i, 74}]; a] (* Michael De Vlieger, Mar 11 2021 *)

Python

from sympy import factorint
def aupton(terms):
  alst, aset = [1], {1}
  for n in range(2, terms+1):
    an = 1
    anm1_digs, anm1_factors = set(str(alst[-1])), set(factorint(alst[-1]))
    while True:
      while an in aset: an += 1
      if set(str(an)) & anm1_digs != set():
        if set(factorint(an)) & anm1_factors == set():
          alst.append(an); aset.add(an); break
      an += 1
  return alst
print(aupton(74)) # Michael S. Branicky, Mar 09 2021