login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A286319 Prime p such that p^2-p-1 or p^2+p-1 is the smallest prime of a twin prime pair. 1
2, 3, 5, 7, 41, 59, 67, 89, 101, 131, 139, 379, 457, 743, 761, 1193, 1201, 1381, 1549, 1567, 1747, 1789, 2137, 2411, 2557, 2647, 2663, 2729, 2731, 3011, 3221, 3251, 3449, 4057, 4159, 4447, 4561, 4751, 5179, 5641, 6173, 6397, 6599, 6833, 7229, 8669, 9059, 9157, 9323 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Union of A088483 and A120364.

3 is the only prime such that p^2-p-1 and p^2+p-1 are both the smallest of a prime twin pair.

For prime p > 3 if p+1 is divisible by 6 then the smallest prime of the prime twin pair is p^2+p-1 and p^2-p-1 if not.

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..50000

EXAMPLE

2^2+2-1=5 and (5,7) is a twin prime pair so a(1)=2.

3^2-3-1=5, 3^2+3-1=11 and (5,7), (11,13) are twin prime pairs so a(2)=3.

5^2+5-1=29 and (29,31) is a twin prime pair so a(3)=5.

7^2-7-1=41 and (41,43) is a twin prime pair so a(4)=7.

MATHEMATICA

sptppQ[n_]:=AllTrue[{n^2-n-1, n^2-n+1}, PrimeQ]||AllTrue[{n^2+n-1, n^2+ n+ 1}, PrimeQ]; Select[Prime[Range[1200]], sptppQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 04 2019 *)

CROSSREFS

Cf. A001359, A088483, A088485, A120364.

Sequence in context: A235395 A090714 A048400 * A090716 A083820 A244556

Adjacent sequences:  A286316 A286317 A286318 * A286320 A286321 A286322

KEYWORD

nonn

AUTHOR

Pierre CAMI, May 11 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 7 11:38 EDT 2022. Contains 355985 sequences. (Running on oeis4.)