A378415 Primes with repeated digits that remain prime when any two of the same-valued digits are deleted.

113, 131, 151, 211, 223, 227, 233, 277, 311, 337, 353, 373, 443, 557, 577, 599, 727, 733, 757, 773, 883, 887, 929, 997, 1009, 1013, 1021, 1031, 1051, 1103, 1117, 1123, 1129, 1153, 1171, 1213, 1223, 1229, 1231, 1291, 1373, 1399, 1447, 1471, 1531, 1553, 1559, 1663, 1667, 1669, 1733, 1777

Offset: 1

Author

Enrique Navarrete, Nov 25 2024

Keywords

• nonn
• base

Comments

Relaxed version of A378081, which contains only 18 terms up to 10^100.

Not a superset of A378081 since this sequence does not contain 257 and 523.

Examples

			114217 is in the sequence since deleting any two of the three 1's gives 4217 and 1427, both of which are prime.
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.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051362, A226108, A378081.

Programs

Python

from sympy import isprime
from itertools import combinations as C
def ok(n):
    if n<100  or not isprime(n) or len(s:=str(n))==len(set(s)): return False
    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:])!="")
print([k for k in range(1800) if ok(k)]) # Michael S. Branicky, Nov 25 2024