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

1,1

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A001097, A001359, A006512, A165966.

Sequence in context: A291747 A024734 A024956 * A338857 A126622 A109332

Adjacent sequences: A105171 A105172 A105173 * A105175 A105176 A105177

Keyword

nonn

Author

Pierre CAMI, Apr 11 2005

Extensions

More terms from Zak Seidov, Oct 07 2009

Status

approved