OFFSET
1,2
EXAMPLE
a(1) = 1 by definition; as 1 has no available divisor yet present in the sequence, we produce a(2) = 3*1 + 1 = 4.
a(2) = 4; as 4 has 2 as its smallest divisor not yet present in the sequence, we have a(3) = 2;
a(3) = 2; as 2 has no available divisor yet present in the sequence, we produce a(4) = 3*2 + 1 = 7.
a(4) = 7; as 7 has no available divisor yet present in the sequence, we produce a(5) = 3*7 + 1 = 22.
a(5) = 22; as 22 has 11 as its smallest divisor not yet present in the sequence, we have a(6) = 11; etc.
MATHEMATICA
a[1]=1; a[n_]:=a[n]=If[(s=Complement[Rest@Divisors@a[n-1], Array[a, n-1]])!={}, Min@s, 3a[n-1]+1]; Array[a, 73] (* Giorgos Kalogeropoulos, Nov 02 2021 *)
PROG
(Python)
from sympy import divisors
terms = [1]
for i in range(100):
for j in divisors(terms[-1]):
if j not in terms:
terms.append(j)
break
else:
terms.append(terms[-1]*3+1)
print(terms) # Gleb Ivanov, Nov 09 2021
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Carole Dubois, Nov 02 2021
STATUS
approved