A108897 Numbers k such that 60*k^2 + 30*k - 30 +- 1 is a twin prime pair.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 21, 22, 37, 39, 40, 41, 42, 51, 53, 54, 59, 64, 71, 80, 82, 83, 94, 102, 103, 105, 106, 110, 114, 118, 128, 143, 144, 156, 166, 167, 169, 172, 183, 192, 193, 199, 218, 222, 224, 227, 234, 235, 236, 253, 258, 259, 265, 266

Offset: 1

Author

Jason Earls, Jul 16 2005

Keywords

• easy
• nonn

Comments

Some consecutive terms in this sequence are (102:103), (105:106), (143:144), ... (1320071:1320072), (1320250:1320251) ... Conjecture: There are infinitely many of these consecutive pairs.

Examples

			1 is in the sequence since 60*1^2 + 30*1 - 30 = 60 and {59, 61} are twin primes.
		

References

• David Wells, Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons, 2005, p. 231.

Links

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

Crossrefs

Cf. A001097, A001359, A006512.

Programs

Mathematica

lst={}; Do[If[PrimeQ[60*n^2+30*n-30-1]&&PrimeQ[60*n^2+30*n-30+1], AppendTo[lst, n]], {n, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 08 2008 *)