A342356 a(1) = 1, a(2) = 10; for n > 2, a(n) is the least positive integer not occurring earlier that shares both a factor and a digit with a(n-1).

1, 10, 12, 2, 20, 22, 24, 4, 14, 16, 6, 26, 28, 8, 18, 15, 5, 25, 35, 30, 3, 33, 36, 32, 34, 38, 48, 40, 42, 21, 27, 57, 45, 50, 52, 54, 44, 46, 56, 58, 68, 60, 62, 64, 66, 63, 39, 9, 69, 90, 70, 7, 77, 147, 49, 84, 74, 37, 333, 93, 31, 124, 72, 75, 51, 17, 102, 80, 78, 76, 86, 82, 88, 98, 91

Offset

1,2

Comments

After 100000 terms the lowest unused number is 18181. The sequence is likely a permutation of the positive integers.

Links

Table of n, a(n) for n=1..75.

Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Mathematica

Block[{a = {1, 10}, m = {1, 0}, 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, 73}]; a] (* Michael De Vlieger, Mar 11 2021 *)

Prog

(Python)
from sympy import factorint
def aupton(terms):
  alst, aset = [1, 10], {1, 10}
  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(75)) # Michael S. Branicky, Mar 09 2021

Crossrefs

Cf. A342366 (share factor but not digit), A239664 (no shared factor or digit), A342367 (share digit but not factor), A184992, A309151, A249591.

Sequence in context: A278856 A316914 A350444 * A338290 A365197 A284229

Adjacent sequences: A342353 A342354 A342355 * A342357 A342358 A342359

Keyword

nonn,base

Author

Scott R. Shannon, Mar 08 2021

Status

approved