A134809 Cyclops primes.

101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 13033, 13037, 13043, 13049, 13063

Offset: 1

Author

Omar E. Pol, Nov 25 2007

Keywords

• nonn
• base

Comments

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

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

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000
• G. L. Honaker, Jr. and Chris K. Caldwell, Prime Curios! 688846502588399
• G. L. Honaker, Jr. and Chris K. Caldwell, Prime Curios! 99194853094755497

Crossrefs

Intersection of prime numbers A000040 and cyclops numbers A134808.

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

Programs

Mathematica

(* First run the program given for A134808 *) Select[Prime[Range[2000]], cyclopsQ] (* Alonso del Arte, Dec 16 2010 *)
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 *)

Python

# cyclops() in A134808
from sympy import isprime
print([c for c in cyclops(upto=13063) if isprime(c)]) # Michael S. Branicky, Jan 05 2021

Extensions

Links added by Omar E. Pol, Mar 25 2011