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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.

%I A048661 #16 Apr 28 2024 11:31:57
%S A048661 0,0,0,0,0,4,12,16,132,308,1096,3704,12984,47008,179660,681608
%N 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.
%H A048661 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_039.htm">Puzzle 39. The Mirrorable Numbers (By Mike Keith)</a>, The Prime Puzzles and Problems Connection.
%o A048661 (Python)
%o A048661 from sympy import isprime
%o A048661 from itertools import count, islice, product
%o A048661 def t(s): return s.translate({ord("2"):ord("5"), ord("5"):ord("2")})
%o A048661 def a(n):
%o A048661     if n < 2: return 0
%o A048661     c = 0
%o A048661     for mid in product("01258", repeat=n-2):
%o A048661         s = "1" + "".join(mid) + "1"
%o A048661         ss = set([s, s[::-1], t(s), t(s[::-1])])
%o A048661         if len(ss) != 4: continue
%o A048661         if all(isprime(int(w)) for w in ss): c += 1
%o A048661     return c
%o A048661 print([a(n) for n in range(1, 11)]) # _Michael S. Branicky_, Apr 27 2024
%Y A048661 Cf. A134996.
%K A048661 base,more,nonn
%O A048661 1,6
%A A048661 _Felice Russo_
%E A048661 a(11)-a(14) from _Sean A. Irvine_, Jun 25 2021
%E A048661 a(15)-a(16) from _Michael S. Branicky_, Apr 27 2024