This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
from itertools import count, islice
from sympy import isprime, nextprime
def agen(): # generator of terms
aset, an, minp = set(), 11, 13
while True:
yield an
aset.add(an)
s = str(an)
targets = set(s[i:i+2] for i in range(len(s)-1))
p = minp
w = str(p)
while p in aset or not any(t in w for t in targets):
p = nextprime(p)
w = str(p)
while minp in aset:
minp = nextprime(minp)
an = p
print(list(islice(agen(), 54))) # Michael S. Branicky, Apr 15 2025
a = {2}; While[ Length[a] < 100, d = IntegerDigits@ Last@ a; p = 2; While[ Intersection[ IntegerDigits@p, d] != {} || MemberQ[a, p], p = NextPrime@ p]; AppendTo[a, p]]; a (* Giovanni Resta, Mar 21 2017 *)
a(3) = 8 is a term because the greatest prime < 10^8 and the least prime > 10^8 are 99999989 and 100000007 respectively, and these have no digits in common. 5 is not a term because the greatest prime < 10^5 and the least prime > 10^5 are 99991 and 100003 respectively, and these have digit 1 in common.
filter:= t -> convert(convert(prevprime(10^t),base,10),set) intersect convert(convert(nextprime(10^t),base,10),set) = {}:
select(filter, [$1..400]);
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