A182811 -id:A182811 - cp's OEIS frontend

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

Omar E. Pol, Nov 25 2007

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).

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

Intersection of prime numbers A000040 and cyclops numbers A134808.

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

(* 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 *)

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

Links added by Omar E. Pol, Mar 25 2011

A182809 Cyclops-Fibonacci numbers.

Original entry on oeis.org

0, 75025, 6557470319842, 14472334024676221, 99194853094755497

Offset: 1

Omar E. Pol, Dec 16 2010

Note that a(5) = 99194853094755497 is the only known Cyclops-Fibonacci prime.
Next term, if it exists, is > Fibonacci(2359000). - Lars Blomberg, May 10 2011
This sequence is similar to A182811 in the sense that both have four positive terms and the only known prime is also the largest known term. - Omar E. Pol, Feb 18 2018
Indices in A000045 are 0, 25, 63, 79, 83. - Michel Marcus and Omar E. Pol, Feb 18 2018

			a(2) = 75025 is in the sequence because 75025 is a Fibonacci number A000045 and 75025 is also a cyclops number A134808.

G. L. Honaker, Jr. and Chris K. Caldwell, Prime Curios! 99194853094755497

Intersection of A000045 and A134808.

Cf. A134809, A138148, A160717, A182811.

(* First run the program given for A134808 *) Select[Fibonacci[Range[10^3]], cyclopsQ] (* Alonso del Arte, Dec 16 2010 *)

a(4) inserted by Alois P. Heinz, Dec 16 2010

cp's OEIS Frontend

A134809 Cyclops primes.

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