A048661 Number of n-digit dihedral primes for which the 4 numbers (n, n upside-down, n in a mirror, n upside-down and mirrored) are distinct.

0, 0, 0, 0, 0, 4, 12, 16, 132, 308, 1096, 3704, 12984, 47008, 179660, 681608

Offset: 1

Author

Felice Russo

Keywords

• base
• more
• nonn

Links

• Carlos Rivera, Puzzle 39. The Mirrorable Numbers (By Mike Keith), The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A134996.

Programs

Python

from sympy import isprime
from itertools import count, islice, product
def t(s): return s.translate({ord("2"):ord("5"), ord("5"):ord("2")})
def a(n):
    if n < 2: return 0
    c = 0
    for mid in product("01258", repeat=n-2):
        s = "1" + "".join(mid) + "1"
        ss = set([s, s[::-1], t(s), t(s[::-1])])
        if len(ss) != 4: continue
        if all(isprime(int(w)) for w in ss): c += 1
    return c
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Apr 27 2024

Extensions

a(11)-a(14) from Sean A. Irvine, Jun 25 2021

a(15)-a(16) from Michael S. Branicky, Apr 27 2024