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

Author

Pierre CAMI, Nov 11 2003

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A088485.

Programs

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 *)

Extensions

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