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.
%I A378415 #23 Dec 03 2024 12:48:44 %S A378415 113,131,151,211,223,227,233,277,311,337,353,373,443,557,577,599,727, %T A378415 733,757,773,883,887,929,997,1009,1013,1021,1031,1051,1103,1117,1123, %U A378415 1129,1153,1171,1213,1223,1229,1231,1291,1373,1399,1447,1471,1531,1553,1559,1663,1667,1669,1733,1777 %N A378415 Primes with repeated digits that remain prime when any two of the same-valued digits are deleted. %C A378415 Relaxed version of A378081, which contains only 18 terms up to 10^100. %C A378415 Not a superset of A378081 since this sequence does not contain 257 and 523. %H A378415 Michael S. Branicky, <a href="/A378415/b378415.txt">Table of n, a(n) for n = 1..10000</a> %e A378415 114217 is in the sequence since deleting any two of the three 1's gives 4217 and 1427, both of which are prime. %e A378415 131371 is not in the sequence since deleting the two 3's gives 1171, which is prime, but deleting two of the three 1's gives 3371, 3137, and 1337, the last one of which is not prime. %o A378415 (Python) %o A378415 from sympy import isprime %o A378415 from itertools import combinations as C %o A378415 def ok(n): %o A378415 if n<100 or not isprime(n) or len(s:=str(n))==len(set(s)): return False %o A378415 return all(isprime(int(t)) for i, j in C(range(len(s)), 2) if s[i]==s[j] and (t:=s[:i]+s[i+1:j]+s[j+1:])!="") %o A378415 print([k for k in range(1800) if ok(k)]) # _Michael S. Branicky_, Nov 25 2024 %Y A378415 Cf. A051362, A226108, A378081. %K A378415 nonn,base %O A378415 1,1 %A A378415 _Enrique Navarrete_, Nov 25 2024