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 A215850 Primes p such that 2*p + 1 divides Lucas(p). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 * A190585 A197276 A211062 Adjacent sequences:  A215847 A215848 A215849 * A215851 A215852 A215853 KEYWORD nonn AUTHOR Arkadiusz Wesolowski, Aug 24 2012 STATUS approved

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Last modified October 23 22:04 EDT 2018. Contains 316541 sequences. (Running on oeis4.)