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A134809 Cyclops primes.

%I A134809 #36 Apr 03 2023 10:36:11
%S A134809 101,103,107,109,307,401,409,503,509,601,607,701,709,809,907,11027,
%T A134809 11047,11057,11059,11069,11071,11083,11087,11093,12011,12037,12041,
%U A134809 12043,12049,12071,12073,12097,13033,13037,13043,13049,13063
%N A134809 Cyclops primes.
%C A134809 Cyclops numbers that are prime numbers: primes with an odd number of digits with middle digit 0 that have only one digit 0.
%C A134809 The only known Fibonacci number in this sequence is 99194853094755497 (see A005478 and A182809).
%C A134809 The only known Lucas number in this sequence is 688846502588399 (see A005479 and A182811).
%H A134809 Harvey P. Dale, <a href="/A134809/b134809.txt">Table of n, a(n) for n = 1..10000</a>
%H A134809 G. L. Honaker, Jr. and Chris K. Caldwell, <a href="https://t5k.org/curios/page.php?number_id=10791">Prime Curios! 688846502588399</a>
%H A134809 G. L. Honaker, Jr. and Chris K. Caldwell, <a href="https://t5k.org/curios/page.php?number_id=10770">Prime Curios! 99194853094755497</a>
%t A134809 (* First run the program given for A134808 *) Select[Prime[Range[2000]], cyclopsQ] (* _Alonso del Arte_, Dec 16 2010 *)
%t A134809 cycQ[n_]:=Module[{idn=IntegerDigits[n],len},len=Length[idn];OddQ[len] && Count[idn,0] == 1 && idn[[(len+1)/2]]==0]; Select[Flatten[Table[Prime[ Range[ PrimePi[10^(2n)+1],PrimePi[10^(2n+1)]]],{n,2}]],cycQ] (* _Harvey P. Dale_, Jun 20 2014 *)
%o A134809 (Python) # cyclops() in A134808
%o A134809 from sympy import isprime
%o A134809 print([c for c in cyclops(upto=13063) if isprime(c)]) # _Michael S. Branicky_, Jan 05 2021
%Y A134809 Intersection of prime numbers A000040 and cyclops numbers A134808.
%Y A134809 Cf. A005478, A005479, A056709, A069675, A182809, A182811.
%K A134809 nonn,base
%O A134809 1,1
%A A134809 _Omar E. Pol_, Nov 25 2007
%E A134809 Links added by _Omar E. Pol_, Mar 25 2011