A088498 Numbers k such that k^2 + k - 1 and k^2 + k + 1 are twin primes and (k + 1)*(k + 1) + k + 1 - 1 and (k + 1)*(k + 1) + k + 1 + 1 are also twin primes.

2, 5, 20, 455, 1364, 2204, 2450, 2729, 8540, 18485, 32198, 32318, 32780, 45863, 61214, 72554, 72560, 82145, 83258, 86603, 91370, 95198, 125333, 149330, 176888, 182909, 185534, 210845, 225665, 226253, 288419, 343160, 350090, 403940, 411500

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

20 is a term since 20^2 + 20 - 1 = 419, 419 and 421 are twin primes, 21^2 + 21 - 1 = 461, and 461 and 463 are also twin primes.

Mathematica

Select[ Range[510397], PrimeQ[ #^2 + # - 1] && PrimeQ[ #^2 + # + 1] && PrimeQ[ #^2 + 3# + 1] && PrimeQ[ #^2 + 3# + 3] & ]
 Select[Range[412000], AllTrue[Flatten[{#^2+#+{1, -1}, (#+1)(#+1)+#+{0, 2}}], PrimeQ]&] (* Harvey P. Dale, Feb 12 2022 *)

Crossrefs

Cf. A088485.

Sequence in context: A216462 A006893 A003163 * A240147 A358556 A293687

Adjacent sequences: A088495 A088496 A088497 * A088499 A088500 A088501

Keyword

base,nonn

Author

Pierre CAMI, Nov 11 2003

Extensions

Corrected and extended by Ray Chandler and Robert G. Wilson v, Nov 12 2003

Status

approved