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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).
3
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
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
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, Mar 09 2021
STATUS
approved