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Cyclops primes.
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%I #36 Apr 03 2023 10:36:11

%S 101,103,107,109,307,401,409,503,509,601,607,701,709,809,907,11027,

%T 11047,11057,11059,11069,11071,11083,11087,11093,12011,12037,12041,

%U 12043,12049,12071,12073,12097,13033,13037,13043,13049,13063

%N Cyclops primes.

%C Cyclops numbers that are prime numbers: primes with an odd number of digits with middle digit 0 that have only one digit 0.

%C The only known Fibonacci number in this sequence is 99194853094755497 (see A005478 and A182809).

%C The only known Lucas number in this sequence is 688846502588399 (see A005479 and A182811).

%H Harvey P. Dale, <a href="/A134809/b134809.txt">Table of n, a(n) for n = 1..10000</a>

%H G. L. Honaker, Jr. and Chris K. Caldwell, <a href="https://t5k.org/curios/page.php?number_id=10791">Prime Curios! 688846502588399</a>

%H G. L. Honaker, Jr. and Chris K. Caldwell, <a href="https://t5k.org/curios/page.php?number_id=10770">Prime Curios! 99194853094755497</a>

%t (* First run the program given for A134808 *) Select[Prime[Range[2000]], cyclopsQ] (* _Alonso del Arte_, Dec 16 2010 *)

%t 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 (Python) # cyclops() in A134808

%o from sympy import isprime

%o print([c for c in cyclops(upto=13063) if isprime(c)]) # _Michael S. Branicky_, Jan 05 2021

%Y Intersection of prime numbers A000040 and cyclops numbers A134808.

%Y Cf. A005478, A005479, A056709, A069675, A182809, A182811.

%K nonn,base

%O 1,1

%A _Omar E. Pol_, Nov 25 2007

%E Links added by _Omar E. Pol_, Mar 25 2011