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A007597 Strobogrammatic primes.

%I A007597 M4800 #32 Apr 03 2023 10:36:09
%S A007597 11,101,181,619,16091,18181,19861,61819,116911,119611,160091,169691,
%T A007597 191161,196961,686989,688889,1008001,1068901,1160911,1180811,1190611,
%U A007597 1191611,1681891,1690691,1880881,1881881,1898681,1908061,1960961,1990661,6081809,6100019,6108019
%N A007597 Strobogrammatic primes.
%C A007597 Primes which are invariant under a 180-degree rotation.
%D A007597 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007597 C. W. Trigg, "Strobogrammatic Primes and Prime Rotative Twins", J. Rec. Math., 15 (1983), 281-282.
%H A007597 Michael S. Branicky, <a href="/A007597/b007597.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..304 from K. D. Bajpai)
%H A007597 C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php/strobogrammatic.html">Strobogrammatic</a>
%H A007597 Ernest G. Hibbs, <a href="https://www.proquest.com/openview/4012f0286b785cd732c78eb0fc6fce80">Component Interactions of the Prime Numbers</a>, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
%H A007597 Wikipedia, <a href="http://en.wikipedia.org/wiki/Strobogrammatic_prime">Strobogrammatic prime</a>
%t A007597 lst = {}; fQ[n_] := Block[{allset = {0, 1, 6, 8, 9}, id = IntegerDigits@n}, Union@ Join[id, allset] == allset && Reverse[id /. {6 -> 9, 9 -> 6}] == id]; Do[ If[ PrimeQ@n && fQ@n, AppendTo[lst, n]], {n, 2000000}]; lst (* _Robert G. Wilson v_, Feb 27 2007 *)
%o A007597 (Python)
%o A007597 from sympy import isprime
%o A007597 from itertools import count, islice, product
%o A007597 def ud(s): return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
%o A007597 def agen():
%o A007597     for d in count(2):
%o A007597         for start in "1689":
%o A007597             for rest in product("01689", repeat=d//2-1):
%o A007597                 left = start + "".join(rest)
%o A007597                 right = ud(left)
%o A007597                 for mid in [[""], ["0", "1", "8"]][d%2]:
%o A007597                     t = int(left + mid + right)
%o A007597                     if isprime(t):
%o A007597                         yield t
%o A007597 print(list(islice(agen(), 33))) # _Michael S. Branicky_, Mar 29 2022
%Y A007597 Cf. A000787.
%K A007597 base,nonn
%O A007597 1,1
%A A007597 _N. J. A. Sloane_, _Robert G. Wilson v_
%E A007597 More terms from _David W. Wilson_
%E A007597 a(31)-a(33) from _K. D. Bajpai_, Jun 23 2017