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

1,6

Links

Table of n, a(n) for n=1..16.

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

Prog

(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

Crossrefs

Cf. A134996.

Sequence in context: A066632 A038242 A370191 * A036047 A356812 A045042

Adjacent sequences: A048658 A048659 A048660 * A048662 A048663 A048664

Keyword

base,more,nonn

Author

Felice Russo

Extensions

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

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

Status

approved