A342367 -id:A342367 - cp's OEIS frontend

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

Scott R. Shannon, Mar 08 2021

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

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

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

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 *)

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

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).

Original entry on oeis.org

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

Scott R. Shannon, Mar 09 2021

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

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

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

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 *)

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

cp's OEIS Frontend

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).

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