A342999 a(n) is always followed by the concatenation of a(n)'s distinct prime factors in increasing order. If this concatenation is already in the sequence, a(n+1) is the smallest term not yet present.

1, 2, 3, 4, 5, 6, 23, 7, 8, 9, 10, 25, 11, 12, 13, 14, 27, 15, 35, 57, 319, 1129, 16, 17, 18, 19, 20, 21, 37, 22, 211, 24, 26, 213, 371, 753, 3251, 28, 29, 30, 235, 547, 31, 32, 33, 311, 34, 217, 731, 1743, 3783, 31397, 36, 38, 219, 373, 39, 313, 40, 41, 42, 237, 379, 43, 44, 45, 46, 223, 47

Offset

1,2

Comments

This is a permutation of the positive terms.

Links

Table of n, a(n) for n=1..69.

Index entries for sequences that are permutations of the natural numbers

Example

a(6) is not = 5, though the only prime factor of a(5) is precisely 5; but as 5 is already in the sequence we must take a(6) = 6, the smallest term not yet present in the sequence.
a(7) = 23 as the prime factors of a(6) = 6 are 2 and 3, which, concatenated in increasing order, give 23;
a(8) is not = 23, though the only prime factor of a(7) is precisely 23; but as 23 is already in the sequence we must take a(8) = 7, the smallest term not yet present in the sequence; etc.

Mathematica

a[1]=1; a[n_]:=a[n]=(g=FromDigits@Flatten[IntegerDigits@*First/@FactorInteger@a[n-1]]; If[FreeQ[k=Array[a, n-1], g], g, Min@Complement[Range@Max[k+1], k]])
Array[a, 100] (* Giorgos Kalogeropoulos, Apr 02 2021 *)

Prog

(Python)
from sympy import primefactors
def aupton(terms):
  alst, aset = [1, 2], {1, 2}
  while len(alst) < terms:
    an = int("".join(map(str, primefactors(alst[-1]))))
    if an in aset:
      an = 1
      while an in aset: an += 1
    alst.append(an); aset.add(an)
  return alst[:terms]
print(aupton(100)) # Michael S. Branicky, Apr 02 2021

Crossrefs

Cf. A084317 (concatenation of the prime factors of n, in increasing order), A037276 (replace n with the concatenation of its prime factors in increasing order).

Sequence in context: A208450 A037333 A183529 * A037404 A037440 A130604

Adjacent sequences: A342996 A342997 A342998 * A343000 A343001 A343002

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Apr 02 2021

Status

approved