A105174 Numbers k such that k*(k+1)/4 - 1 and k*(k+1)/4 + 1 are twin primes.

8, 15, 23, 24, 71, 80, 104, 128, 159, 216, 231, 264, 288, 303, 336, 344, 455, 495, 528, 543, 560, 608, 624, 680, 744, 816, 840, 879, 896, 1016, 1104, 1311, 1415, 1440, 1464, 1520, 1584, 1599, 1751, 1871, 1896, 1920, 1976, 2015, 2016, 2055, 2088, 2103, 2175

Offset: 1

Author

Pierre CAMI, Apr 11 2005

Keywords

• nonn

Comments

The twin primes are = (sum of numbers from 1 to k)/2 -1 and +1.

Examples

			8*9/4=18, 17 and 19 twin primes so a(1)=8
15*16/4=60, 59 and 61 twin primes so a(2)=15
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A001097, A001359, A006512, A165966.

Programs

Mathematica

Select[Range[2200],AllTrue[(#(#+1))/4+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 01 2015 *)

Extensions

More terms from Zak Seidov, Oct 07 2009