A182811 Cyclops-Lucas numbers.

64079, 1860498, 4870847, 688846502588399

Offset: 1

Author

Omar E. Pol, Dec 20 2010

Keywords

• nonn
• base
• hard
• more

Comments

a(4) = 688846502588399 is the only known Cyclops-Lucas prime.

It seems likely that these four are the only terms. There are no further terms below Lucas(10^7), and that number in decimal contains 208435 zeros (with ~208988 expected assuming normality), whereas a member of this sequence must have only 1. - D. S. McNeil, Dec 21 2010

This sequence is similar to A182809 in the sense that both have four positive terms and the only known prime is also the largest known term. - Omar E. Pol, Dec 21 2010

Indices in A000032 are 23, 30, 32, 71. - Michel Marcus and Omar E. Pol, Feb 18 2018

Examples

			a(1) = 64079 is in the sequence because 64079 is a Lucas number and it is also a cyclops number.
		

Links

• G. L. Honaker, Jr. and Chris K. Caldwell, Prime Curios! 688846502588399

Crossrefs

Intersection of A000032 and A134808.

Cf. A005479, A134809, A182809.

Programs

Mathematica

(* First run the program given for A134808 *) Select[LucasL[Range[10^3]], cyclopsQ] (* Alonso del Arte, Dec 20 2010 *)
Select[LucasL[Range[500]],OddQ[IntegerLength[#]]&&DigitCount[#,10,0]==1&&IntegerDigits[#][[(IntegerLength[#]+1)/2]]==0&] (* Harvey P. Dale, Jul 01 2017 *)

Formula

Intersection of A000032 and A134808.