A074304 -id:A074304 - cp's OEIS frontend

A074281 Primes of the form Lucas(2*n)/3.

41, 281, 90481, 29134601, 3020733700601, 313195711516578281, 5280544535667472291277149119296546201, 547497418496144666543167613835090178297001

Offset: 1

Shane Findley, Sep 21 2002

nonn

The next term has 96 digits. - Harvey P. Dale, Apr 29 2011.

			Lucas(2*5)=3*41, Lucas(2*7)=3*281, Lucas(2*13)=3*90481.

Vincenzo Librandi, Table of n, a(n) for n = 1..16
Ron Knott, The Mathematics of the Fibonacci series.
Ron Knott, Pi and the Fibonacci Numbers.

Values of n are given in A074304.

Select[Table[LucasL[2n]/3,{n,400}],PrimeQ]  (* Harvey P. Dale, Apr 29 2011 *)

A355980 Indices of primes in A049685.

Original entry on oeis.org

2, 3, 6, 9, 15, 21, 44, 50, 114

Offset: 1

R. J. Mathar, Jul 22 2022

Related to the search of solutions of the pair of congruences p^2 == -5 (mod q), q^2 == -5 (mod p).

Cosgrave and Dilcher list terms up to 25000, including probable primes.

J. B. Cosgrave and K. Dilcher, Pairs of reciprocal quadratic congruences involving primes, Fib. Quart. 51 (2) (2013) 98, after Theorem 4.

Cf. A049685, A074281, A074304.

A074281(n) = A049685(a(n)).

a(n) = (A074304(n)-1)/2.

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

Original entry on oeis.org

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

Offset: 1

Alexander Adamchuk, May 14 2007, May 16 2007

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

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

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

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

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

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A074281 Primes of the form Lucas(2*n)/3.

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A355980 Indices of primes in A049685.

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

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