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A381130 a(n) is the smallest prime not yet in the sequence that contains a substring of size 2 from a(n-1); a(1)=11.

%I A381130 #9 Apr 16 2025 05:31:32
%S A381130 11,113,13,131,31,311,211,421,521,523,23,223,227,127,271,71,571,157,
%T A381130 151,251,257,457,557,577,277,677,67,167,163,263,269,569,563,463,461,
%U A381130 61,613,137,37,337,233,239,139,313,317,17,173,73,373,379,79,179,479,47
%N A381130 a(n) is the smallest prime not yet in the sequence that contains a substring of size 2 from a(n-1); a(1)=11.
%H A381130 Michael S. Branicky, <a href="/A381130/b381130.txt">Table of n, a(n) for n = 1..10000</a>
%o A381130 (Python)
%o A381130 from itertools import count, islice
%o A381130 from sympy import isprime, nextprime
%o A381130 def agen(): # generator of terms
%o A381130     aset, an, minp = set(), 11, 13
%o A381130     while True:
%o A381130         yield an
%o A381130         aset.add(an)
%o A381130         s = str(an)
%o A381130         targets = set(s[i:i+2] for i in range(len(s)-1))
%o A381130         p = minp
%o A381130         w = str(p)
%o A381130         while p in aset or not any(t in w for t in targets):
%o A381130             p = nextprime(p)
%o A381130             w = str(p)
%o A381130         while minp in aset:
%o A381130             minp = nextprime(minp)
%o A381130         an = p
%o A381130 print(list(islice(agen(), 54))) # _Michael S. Branicky_, Apr 15 2025
%Y A381130 Cf. A107801, A262323.
%K A381130 nonn,base
%O A381130 1,1
%A A381130 _Enrique Navarrete_, Feb 14 2025