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Numbers k such that 3*5^(2*k) - 3*5^k + 1 is prime.
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%I #23 Oct 09 2024 15:27:17

%S 1,2,8,25,41,66,108,318,498,546,557,846,3780,26370,29305,31482,32905

%N Numbers k such that 3*5^(2*k) - 3*5^k + 1 is prime.

%C a(14) > 10^4. - _Daniel Suteu_, Feb 13 2019

%H Eric L. F. Roettger, <a href="https://web.archive.org/web/20230227201214/http://people.ucalgary.ca/~hwilliam/files/A_Cubic_Extention_of_the_Lucas_Functions.pdf">A Cubic Extension of the Lucas Functions</a>, Ph. D. Dissertation, Dept. Math. and Statistics, Univ. Calgary, 2009 (see page 196).

%t Select[Range[0, 3000], PrimeQ[3 5^(2 #) - 3 5^# + 1]&]

%o (PARI) is(n)=ispseudoprime(3*5^(2*n)-3*5^n+1) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A057917.

%K nonn,more

%O 1,2

%A _Vincenzo Librandi_, Jul 14 2013

%E a(13) from _Daniel Suteu_, Feb 13 2019

%E a(14)-a(17) from _Michael S. Branicky_, Oct 08 2024