A348881 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.

1, 2, 5, 14, 7, 20, 4, 11, 32, 8, 23, 68, 17, 50, 10, 29, 86, 43, 128, 16, 47, 140, 28, 83, 248, 31, 92, 46, 137, 410, 41, 122, 61, 182, 13, 38, 19, 56, 167, 500, 25, 74, 37, 110, 22, 65, 194, 97, 290, 58, 173, 518, 259, 776, 388, 1163, 3488, 109, 326, 163, 488, 244, 731, 2192, 274, 821, 2462, 1231, 3692, 26

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1) = 1 by definition; as 1 has no divisor not yet present in the sequence, we produce a(2) = 3*1 - 1 = 2.
a(2) = 2; as 2 has no divisor not yet present in the sequence, we produce a(3) = 3*2 - 1 = 5.
a(3) = 5; as 5 has no divisor not yet present in the sequence, we produce a(4) = 3*5 - 1 = 14.
a(4) = 14; as 14 has 7 as its smallest divisor not yet present in the sequence, we have a(5) = 7.
a(5) = 7; as 7 has no divisor not yet present in the sequence, we produce a(6) = 3*7 - 1 = 20.

Maple

S:= {1}: R:= 1: a:= 1:
for i from 2 to 100 do
  Q:= numtheory:-divisors(a) minus S;
  if Q = {} then a:= 3*a-1 else a:= min(Q) fi;
  R:= R, a; S:= S union {a};
od:
R; # Robert Israel, Feb 27 2025

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, 70] (* 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, A348873.

Sequence in context: A016737 A279253 A279958 * A324982 A289682 A151854

Adjacent sequences: A348878 A348879 A348880 * A348882 A348883 A348884

Keyword

nonn

Author

Carole Dubois and Eric Angelini, Nov 02 2021

Extensions

Edited by Robert Israel, Feb 27 2025

Status

approved