login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A265006 Twin prime pairs of the form (k^2 + k - 1, k^2 + k + 1). 2
5, 7, 11, 13, 29, 31, 41, 43, 71, 73, 239, 241, 419, 421, 461, 463, 599, 601, 1481, 1483, 1721, 1723, 2549, 2551, 2969, 2971, 3539, 3541, 4421, 4423, 8009, 8011, 10301, 10303, 17291, 17293, 19181, 19183, 20021, 20023, 23561, 23563, 24179, 24181, 27059, 27061, 31151, 31153, 35531, 35533 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is a subset of A002327 and A002383 taken together. Note that 3 is not a member, as the pairing (3, 5) is excluded as defined, as 3 and 5 associate to different centers.

The corresponding n are in A088485, and the first bisection is A088486.

The average of each twin prime pair is an oblong number (A002378). - Michel Marcus, Feb 04 2017

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..3594 from G. C. Greubel)

EXAMPLE

For k = 6, k^2 + k = 6^2 + 6 = 42, and (41,43) is a twin prime pair, so 41 and 43 are in the sequence.

MATHEMATICA

{#^2 + # - 1, #^2 + # + 1} & /@ Select[Range@ 200, PrimeQ[#^2 + # - 1] && PrimeQ[#^2 + # + 1] &] // Flatten (* Michael De Vlieger, Nov 30 2015 *)

Flatten[Select[Table[n^2 + n + {-1, 1}, {n, 0, 200}], And@@PrimeQ[#] &]] (* Vincenzo Librandi, Feb 05 2017 *)

PROG

(PARI) genit()={my(maxx=1000); n=0; while(n<maxx, n+=1; q=n^2+n; if( isprime(q-1)&&isprime(q+1), print1(q-1, ", ", q+1, ", "))); }

(MAGMA) &cat[[n^2+n-1, n^2+n+1]: n in [0..250]| IsPrime(n^2+n-1) and IsPrime(n^2+n+1)]; // Vincenzo Librandi, Feb 05 2017

CROSSREFS

Cf. A002327, A002378, A002383, A088485, A088486.

Sequence in context: A265780 A135774 A180946 * A135930 A163429 A339953

Adjacent sequences:  A265003 A265004 A265005 * A265007 A265008 A265009

KEYWORD

nonn,easy,tabf

AUTHOR

Bill McEachen, Nov 29 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 03:59 EST 2021. Contains 349530 sequences. (Running on oeis4.)