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A182811 Cyclops-Lucas numbers. 2

%I #29 Apr 03 2023 10:36:12

%S 64079,1860498,4870847,688846502588399

%N Cyclops-Lucas numbers.

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

%C 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

%C 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

%C Indices in A000032 are 23, 30, 32, 71. - _Michel Marcus_ and _Omar E. Pol_, Feb 18 2018

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

%F Intersection of A000032 and A134808.

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

%t (* First run the program given for A134808 *) Select[LucasL[Range[10^3]], cyclopsQ] (* _Alonso del Arte_, Dec 20 2010 *)

%t Select[LucasL[Range[500]],OddQ[IntegerLength[#]]&&DigitCount[#,10,0]==1&&IntegerDigits[#][[(IntegerLength[#]+1)/2]]==0&] (* _Harvey P. Dale_, Jul 01 2017 *)

%Y Intersection of A000032 and A134808.

%Y Cf. A005479, A134809, A182809.

%K nonn,base,hard,more

%O 1,1

%A _Omar E. Pol_, Dec 20 2010

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)