A265006 Twin prime pairs of the form (k^2 + k - 1, k^2 + k + 1).

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

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