A372407 - OEIS

%I #15 May 12 2024 11:46:45

%S 2,3,5,7,17,11,13,19,29,23,43,41,31,37,47,67,61,71,73,53,59,79,89,83,

%T 283,223,227,127,107,101,103,109,139,131,137,157,151,181,191,193,113,

%U 163,167,197,97,397,307,317,311,211,241,251,257,277,271,281,881,811,821,421,401,409,419,439

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

%C The sequence is a permutation of the prime numbers.

%H Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2024/04/prime-padlock.html">Prime combination lock</a>, Personal blog, April 2024.

%e The Levenshtein distance = 1 between 2 and 3, 3 and 5, 5 and 7, 7 and 17, 17 and 11, 11 and 13, etc.

%e No smaller prime than 17 was possible for a(5).

%t 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]

%o (Python)

%o from sympy import isprime

%o from itertools import islice

%o from Levenshtein import distance as Ld

%o def agen(): # generator of terms

%o     an, aset, mink = 2, {2}, 3

%o     while True:

%o         yield an

%o         s, k = str(an), mink

%o         while k in aset or Ld(s, str(k)) != 1 or not isprime(k): k += 1

%o         an = k

%o         aset.add(k)

%o         while mink in aset or not isprime(mink): mink += 1

%o print(list(islice(agen(), 70))) # _Michael S. Branicky_, Apr 29 2024

%Y Cf. A000040, A118763, A372408.

%K base,nonn

%O 1,1

%A _Eric Angelini_ and _Giorgos Kalogeropoulos_, Apr 29 2024