A088483 Primes p such that p^2+p-1 and p^2+p+1 are twin primes.

2, 3, 5, 41, 59, 89, 101, 131, 743, 761, 1193, 2411, 2663, 2729, 3011, 3221, 3251, 3449, 4751, 6173, 6599, 6833, 7229, 8669, 9059, 9323, 9521, 9719, 9743, 10151, 10781, 11549, 11933, 12143, 12251, 12473, 12641, 13553, 13613, 14939, 15569, 16301

Offset

1,1

Comments

Also primes in A155173 = Short leg A of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs... - Vladimir Joseph Stephan Orlovsky, Jan 21 2009

All terms >3 are congruent to 5 modulo 6. - Zak Seidov, Mar 21 2014

Intersection of A000040 and A088485. - Danny Rorabaugh, May 15 2017

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

a(7) = 101: 101*101 + 101 - 1 = 10301, 10301 and 10303 twin primes.

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[p1=p*p+p-1]&&PrimeQ[p1+2], AppendTo[lst, p]], {n, 2*7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 21 2009 *)
Select[Prime[Range[2000]], AllTrue[#^2+#+{1, -1}, PrimeQ]&] (* Harvey P. Dale, Feb 22 2023 *)

Prog

(PARI) forprime(p=2, 1e5, if(isprime(p^2+p-1)&&isprime(p^2+p+1), print1(p", "))) \\ Charles R Greathouse IV, Dec 27 2011

Crossrefs

Cf. A001097, A088484, A088485.

Sequence in context: A215321 A215309 A215105 * A235681 A322748 A224781

Adjacent sequences: A088480 A088481 A088482 * A088484 A088485 A088486

Keyword

nonn

Author

Pierre CAMI, Nov 09 2003

Status

approved