A215850 Primes p such that 2*p + 1 divides Lucas(p).

5, 29, 89, 179, 239, 359, 419, 509, 659, 719, 809, 1019, 1049, 1229, 1289, 1409, 1439, 1499, 1559, 1889, 2039, 2069, 2129, 2339, 2399, 2459, 2549, 2699, 2819, 2939, 2969, 3299, 3329, 3359, 3389, 3449, 3539, 3779, 4019, 4349, 4409, 4919, 5039, 5279, 5399, 5639

Offset

1,1

Comments

An equivalent definition of this sequence: 5 together with primes p such that p == -1 (mod 30) and 2*p + 1 is also prime.

Sequence without the initial 5 is the intersection of A005384 and A132236.

These numbers do not occur in A137715.

From Arkadiusz Wesolowski, Aug 25 2012: (Start)

The sequence contains numbers like 1409 which are in A053027.

a(n) is in A002515 if and only if a(n) is congruent to -1 mod 60. (End)

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

C. K. Caldwell, "Top Twenty" page, Lucas cofactor

Eric Weisstein's World of Mathematics, Lucas Number

Example

29 is in the sequence since it is prime and 59 is a factor of Lucas(29) = 1149851.

Mathematica

Select[Prime@Range[740], Divisible[LucasL[#], 2*# + 1] &]
Prepend[Select[Range[29, 5639, 30], PrimeQ[#] && PrimeQ[2*# + 1] &], 5]

Prog

(Magma) [5] cat [n: n in [29..5639 by 30] | IsPrime(n) and IsPrime(2*n+1)];
(PARI) is_A215850(n)=isprime(n)&!real((Mod(2, 2*n+1)+quadgen(5))*quadgen(5)^n) \\ - M. F. Hasler, Aug 25 2012

Crossrefs

Supersequence of A230809. Cf. A000032, A132236.

Sequence in context: A272650 A050409 A111937 * A308396 A190585 A197276

Adjacent sequences: A215847 A215848 A215849 * A215851 A215852 A215853

Keyword

nonn

Author

Arkadiusz Wesolowski, Aug 24 2012

Status

approved