A348871 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 tt (t concatenated to itself). If tt doesn't produce a new d, we extend the sequence with ttt, etc. See the Comments section for more details.

1, 11, 111, 3, 33, 333, 9, 99, 999, 27, 2727, 101, 101101, 7, 77, 777, 21, 2121, 303, 303303, 13, 1313, 131313, 37, 3737, 373737, 39, 3939, 393939, 63, 6363, 707, 707707, 49, 4949, 494949, 91, 9191, 919191, 147, 147147, 143, 143143, 121, 121121, 847, 847847, 539, 539539, 343, 343343, 637, 637637, 169, 169169, 1001

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Example

a(1) = 1 by definition. As a(1) has no available divisor not yet present in the sequence, we concatenate 1 with itself to produce 11.
a(2) = 11; as 11 has no available divisor not yet present in the sequence, we concatenate 1 with 11 to produce 111.
a(3) = 111; as 111 produces the new divisor 3, we have a(4) = 3; etc.

Mathematica

a[1]=1; t=1; a[n_]:=a[n]=If[b=FromDigits[Join@@IntegerDigits/@Table[a[n-t], t+1]]; Length[d=Divisors@a[n-1]]>2, If[(s=Complement[Most@Rest@d, Array[a, n-1]])!={}, t=1; Min@s, t++; b], t++; b]; Array[a, 56] (* Giorgos Kalogeropoulos, Nov 03 2021 *)

Prog

(Python)
from sympy import divisors
terms = [1]
c = 1
for i in range(100):
    for j in divisors(terms[-1]):
        if j not in terms:
            terms.append(j)
            c = j
            break
    else:
        terms.append(int(str(terms[-1]) + str(c)))
print(terms) # Gleb Ivanov, Nov 09 2021

Crossrefs

Cf. A000005.

Sequence in context: A356329 A055016 A259372 * A004287 A061493 A093788

Adjacent sequences: A348868 A348869 A348870 * A348872 A348873 A348874

Keyword

nonn

Author

Eric Angelini and Carole Dubois, Nov 02 2021

Status

approved