A378563 Primes that remain prime if any three of their digits are deleted.

2237, 2273, 2333, 2357, 2377, 2557, 2753, 2777, 3253, 3257, 3323, 3373, 3527, 3533, 3557, 3727, 3733, 5227, 5233, 5237, 5273, 5323, 5333, 5527, 5557, 5573, 5737, 7237, 7253, 7333, 7523, 7537, 7573, 7577, 7723, 7727, 7753, 7757, 11113, 11117, 11119, 11131, 11171, 11173, 11197

Offset

1,1

Comments

Any 4-digit term has all digits prime (cf. A019546).

The corresponding sequence for two digits deleted contains only 18 terms up to 10^100 (Cf. A378081).

Any term >= 10000 must have its last four digits be from {1, 3, 7, 9}. - Michael S. Branicky, Dec 01 2024

Links

Table of n, a(n) for n=1..45.

Example

43117 is in the sequence since upon deleting any three digits we get 43, 31, 11, 17 and 47, all of which are prime.

Prog

(Python)
from sympy import isprime
from itertools import combinations as C
def ok(n):
    if n < 1000 or not isprime(n): return False
    s = str(n)
    return all(isprime(int(t)) for i, j, k in C(range(len(s)), 3) if (t:=s[:i]+s[i+1:j]+s[j+1:k]+s[k+1:])!="")
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Dec 01 2024

Crossrefs

Cf. A019546, A051362, A378081.

Sequence in context: A279661 A288846 A289454 * A372248 A079013 A186865

Adjacent sequences: A378558 A378560 A378561 * A378564 A378565 A378566

Keyword

nonn,base,less,new

Author

Enrique Navarrete, Nov 30 2024

Status

approved