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