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

5, 17, 19, 41, 43, 71, 1511, 2339, 3469, 4787, 7211, 9781, 14431

Offset: 1

Author

Alexander Adamchuk, May 14 2007, May 16 2007

Keywords

• less
• more
• nonn

Comments

L(m) = Lucas(m) = Fibonacci(m-1) + Fibonacci(m+1). 7 = L(4) divides L(4*(1+2m)) since L(4m) = L(4)*L(4*(m-1)) - L(4*(m-2)).

Integer k is in this sequence iff k is prime and 4k belongs to A085726. - Max Alekseyev, May 16 2010

a(14) > 60000. - Michael S. Branicky, Aug 01 2024

Crossrefs

Cf. A000032, A001606 (indices of prime Lucas numbers).

Cf. A074304 (numbers k such that Lucas(2k)/3 is prime).

Programs

Mathematica

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

Extensions

a(7) - a(10) from Stefan Steinerberger, May 17 2007

a(11) from Max Alekseyev, Nov 25 2007

a(12) from Alexander Adamchuk, May 15 2010

a(13) from Michael S. Branicky, Aug 01 2024