

A182811


CyclopsLucas numbers.


2




OFFSET

1,1


COMMENTS

a(4) = 688846502588399 is the only known CyclopsLucas 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


LINKS

Table of n, a(n) for n=1..4.
G. L. Honaker, Jr. and Chris K. Caldwell, Prime Curios! 688846502588399


FORMULA

Intersection of A000032 and A134808.


EXAMPLE

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


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 *)


CROSSREFS

Intersection of A000032 and A134808.
Cf. A005479, A134809, A182809.
Sequence in context: A054738 A250617 A031859 * A236702 A224827 A234128
Adjacent sequences: A182808 A182809 A182810 * A182812 A182813 A182814


KEYWORD

nonn,base,hard,more


AUTHOR

Omar E. Pol, Dec 20 2010


STATUS

approved



