A342366 a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier that shares a factor but not a digit with a(n-1).

1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 20, 14, 7, 21, 30, 15, 24, 16, 22, 11, 33, 18, 26, 13, 52, 34, 17, 68, 32, 40, 25, 60, 27, 36, 28, 35, 42, 38, 19, 57, 39, 45, 63, 48, 50, 44, 55, 66, 51, 69, 23, 46, 58, 29, 87, 54, 62, 31, 248, 56, 49, 70, 64, 72, 80, 65, 78, 90, 74, 82, 41, 205, 164, 88, 76, 84

Offset

1,2

Comments

After 100000 terms the lowest unused number is 1523. It is unknown if the sequence is a permutation of the positive integers.

Links

Table of n, a(n) for n=1..76.

Scott R. Shannon, Image of the first 10000 terms. The green line is a(n) = n.

Mathematica

Block[{a = {1, 2}, m = {2}, 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, 2], {1, 2}
  for n in range(3, 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(76)) # Michael S. Branicky, Mar 09 2021

Crossrefs

Cf. A342356 (share factor and digit), A239664 (no shared factor or digit), A342367 (share digit but not factor), A184992, A309151, A249591.

Sequence in context: A357994 A357942 A255348 * A336946 A357777 A348086

Adjacent sequences: A342363 A342364 A342365 * A342367 A342368 A342369

Keyword

nonn,base

Author

Scott R. Shannon, Mar 09 2021

Status

approved