A088486 -id:A088486 - cp's OEIS frontend

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

Bill McEachen, Nov 29 2015

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

			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.

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

Cf. A002327, A002378, A002383, A088485, A088486, A306889.

&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

{#^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 *)

PARI
```
genit()={my(maxx=1000);n=0;while(n
				
```

a(2n-1) = A088486(n). a(2n)=2+a(2n-1).

A255229 Integers n such that n^2 - 1 is the difference of the squares of twin primes.

Original entry on oeis.org

5, 7, 11, 13, 17, 31, 41, 43, 49, 77, 83, 101, 109, 119, 133, 179, 203, 263, 277, 283, 307, 311, 329, 353, 377, 407, 413, 419, 431, 437, 463, 473, 493, 577, 581, 619, 629, 703, 757, 791, 811, 907, 911, 913, 991, 1001, 1037, 1061, 1103, 1121, 1249, 1289, 1337, 1373, 1441, 1457, 1487, 1523, 1597, 1651, 1781

Offset: 1

Neri Gionata, Feb 18 2015

nonn

			31^2 - 1 = 241^2 - 239^2, and (239, 241) is a twin prime pair, so 31 is in the sequence.

Cf. A088486 (corresponding lesser twin primes), A111046.

lst={};f[n_]:=Sqrt[Prime[n]^2-NextPrime[Prime[n],-1]^2+1];
Do[If[Prime[n]-NextPrime[Prime[n],-1]==2&&IntegerQ[f[n]],AppendTo[lst,f[n]]],{n,3,10^5}];lst (* Ivan N. Ianakiev, Mar 30 2015 *)

lista(nn) = {forprime(p=3, nn, q = precprime(p-1); if (((p-q) == 2) && issquare(d=p^2-q^2+1), print1(sqrtint(d), ", ")); ); } \\ Michel Marcus, Feb 18 2015

cp's OEIS Frontend

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

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