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

Author

Arkadiusz Wesolowski, Aug 24 2012

Keywords

• nonn

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)

Examples

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

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

Crossrefs

Supersequence of A230809. Cf. A000032, A132236.

Programs

Magma

[5] cat [n: n in [29..5639 by 30] | IsPrime(n) and IsPrime(2*n+1)];

Mathematica

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

PARI

is_A215850(n)=isprime(n)&!real((Mod(2,2*n+1)+quadgen(5))*quadgen(5)^n) \\ - M. F. Hasler, Aug 25 2012