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

1,2

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

Table of n, a(n) for n=1..74.

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A123895 A147519 A303657 * A303879 A305947 A100830

Adjacent sequences: A342364 A342365 A342366 * A342368 A342369 A342370

Keyword

nonn,base

Author

Scott R. Shannon, Mar 09 2021

Status

approved