A372407 a(n) = smallest prime not occurring earlier having in decimal representation to its predecessor Levenshtein distance = 1.

2, 3, 5, 7, 17, 11, 13, 19, 29, 23, 43, 41, 31, 37, 47, 67, 61, 71, 73, 53, 59, 79, 89, 83, 283, 223, 227, 127, 107, 101, 103, 109, 139, 131, 137, 157, 151, 181, 191, 193, 113, 163, 167, 197, 97, 397, 307, 317, 311, 211, 241, 251, 257, 277, 271, 281, 881, 811, 821, 421, 401, 409, 419, 439

Offset: 1

Author

Eric Angelini and Giorgos Kalogeropoulos, Apr 29 2024

Keywords

• base
• nonn

Comments

The sequence is a permutation of the prime numbers.

Examples

			The Levenshtein distance = 1 between 2 and 3, 3 and 5, 5 and 7, 7 and 17, 17 and 11, 11 and 13, etc.
No smaller prime than 17 was possible for a(5).
		

Links

• Eric Angelini, Prime combination lock, Personal blog, April 2024.

Crossrefs

Cf. A000040, A118763, A372408.

Programs

Mathematica

a[1]=2;a[n_]:=a[n]=(k=2;While[MemberQ[Array[a,n-1],k]|| EditDistance[ToString@k, ToString@a[n-1]]!=1,k=NextPrime@k];k);Array[a,68]

Python

from sympy import isprime
from itertools import islice
from Levenshtein import distance as Ld
def agen(): # generator of terms
    an, aset, mink = 2, {2}, 3
    while True:
        yield an
        s, k = str(an), mink
        while k in aset or Ld(s, str(k)) != 1 or not isprime(k): k += 1
        an = k
        aset.add(k)
        while mink in aset or not isprime(mink): mink += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Apr 29 2024