A348873 After a(1) = 1, the sequence is always extended with the smallest divisor d (not yet present in the sequence) of the last term t. If d doesn't exist, we extend the sequence with 3*t + 1 and repeat. See the Comments section for more details.

1, 4, 2, 7, 22, 11, 34, 17, 52, 13, 40, 5, 16, 8, 25, 76, 19, 58, 29, 88, 44, 133, 400, 10, 31, 94, 47, 142, 71, 214, 107, 322, 14, 43, 130, 26, 79, 238, 119, 358, 179, 538, 269, 808, 101, 304, 38, 115, 23, 70, 35, 106, 53, 160, 20, 61, 184, 46, 139, 418, 209, 628, 157, 472, 59, 178, 89, 268, 67, 202, 607, 1822, 911

Offset

1,2

Links

Table of n, a(n) for n=1..73.

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

Cf. A348871, A348872.

Sequence in context: A211941 A050105 A367209 * A128333 A201414 A199814

Adjacent sequences: A348870 A348871 A348872 * A348874 A348875 A348876

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Nov 02 2021

Status

approved