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A129745 Numbers n such that Lucas(4n)/7 is prime. 0

%I

%S 5,17,19,41,43,71,1511,2339,3469,4787,7211,9781

%N Numbers n such that Lucas(4n)/7 is prime.

%C L(k) = Lucas(k) = Fibonacci(k-1) + Fibonacci(k+1). 7 = L(4) divides L(4(1+2k)) since L(4n) = L(4)*L(4(n-1)) - L(4(n-2)).

%C Integer n is in this sequence iff n is prime and 4n belongs to A085726. [From _Max Alekseyev_, May 16 2010]

%t a=7; b=47; Do[ c=7b-a; a=b; b=c; If[ PrimeQ[c/7], Print[n] ], {n, 3, 100}]

%Y Cf. A000032, A001606 = Indices of prime Lucas numbers. Cf. A074304 = numbers n such that Lucas(2n)/3 is prime.

%K less,more,nonn

%O 1,1

%A _Alexander Adamchuk_, May 14 2007, May 16 2007

%E a(7) - a(10) from _Stefan Steinerberger_, May 17 2007

%E a(11) from _Max Alekseyev_, Nov 25 2007

%E a(12) from _Alexander Adamchuk_, May 15 2010

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Last modified February 21 21:58 EST 2020. Contains 332113 sequences. (Running on oeis4.)