

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
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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(q1)&&isprime(q+1), print1(q1, ", ", q+1, ", "))); }
(MAGMA) &cat[[n^2+n1, n^2+n+1]: n in [0..250] IsPrime(n^2+n1) 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



