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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.
1
0, 0, 0, 0, 0, 4, 12, 16, 132, 308, 1096, 3704, 12984, 47008, 179660, 681608
OFFSET
1,6
LINKS
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
KEYWORD
base,more,nonn
AUTHOR
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