A230809 -id:A230809 - cp's OEIS frontend

A142799 Primes congruent to 59 mod 60.

59, 179, 239, 359, 419, 479, 599, 659, 719, 839, 1019, 1259, 1319, 1439, 1499, 1559, 1619, 1979, 2039, 2099, 2339, 2399, 2459, 2579, 2699, 2819, 2879, 2939, 2999, 3119, 3299, 3359, 3539, 3659, 3719, 3779, 4019, 4079, 4139, 4259, 4679, 4799, 4919, 5039, 5099

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Supersequence of A230809. Cf. A000040.

[p: p in PrimesUpTo(6000) | p mod 60 eq 59 ]; // Vincenzo Librandi, Sep 04 2012

Select[Prime[Range[900]], MemberQ[{59}, Mod[#, 60]] &] (* Vincenzo Librandi, Sep 04 2012 *)
Select[Range[59,5250,60],PrimeQ] (* Harvey P. Dale, Jun 09 2024 *)

is(n)=isprime(n) && n%60==59 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 16n log n. - Charles R Greathouse IV, Jul 02 2016

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

Original entry on oeis.org

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

Arkadiusz Wesolowski, Aug 24 2012

nonn

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)

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

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

Supersequence of A230809. Cf. A000032, A132236.

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

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

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

A239548 Primes p such that gcd(Lucas(p), Mersenne(p)) > 1.

Original entry on oeis.org

2, 179, 239, 359, 419, 487, 659, 719, 883, 1013, 1019, 1439, 1459, 1499, 1559, 1723, 1871, 1993, 2039, 2339, 2399, 2459, 2593, 2699, 2819, 2939, 3041, 3299, 3329, 3359, 3539, 3779, 4019, 4813, 4919, 4957, 5039, 5231, 5261, 5279, 5399, 5639, 6011, 6353, 6373

Offset: 1

Arkadiusz Wesolowski, Mar 21 2014

nonn

			239 is in the sequence since it is prime and 479 is a prime factor of both Lucas(239) and Mersenne(239) = 2^239 - 1.

Eric Weisstein's World of Mathematics, Lucas Number
Eric Weisstein's World of Mathematics, Mersenne Number

Supersequence of A230809.

Cf. A000032, A001348.

[p: p in PrimesUpTo(6500) | Gcd(Lucas(p),2^p-1) gt 1];

for(p=2, 6373, if(isprime(p)&&gcd(fibonacci(p-1)+fibonacci(p+1), 2^p-1)>1, print1(p, ", ")));

cp's OEIS Frontend

A142799 Primes congruent to 59 mod 60.

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

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A239548 Primes p such that gcd(Lucas(p), Mersenne(p)) > 1.

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