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

Author

Eric Angelini and Carole Dubois, Apr 02 2021

Keywords

• base
• nonn

Comments

This is a permutation of the positive terms.

Examples

			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.
		

Links

• Index entries for sequences that are permutations of the natural numbers

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).

Programs

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 *)

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