A172494 Numbers k with (p,p+2) = ((2*k)^3/2 - 1,(2*k)^3/2 + 1) is a twin prime pair.

1, 3, 87, 195, 243, 297, 408, 495, 522, 528, 573, 600, 798, 885, 903, 957, 1038, 1053, 1110, 1200, 1233, 1293, 1302, 1308, 1368, 1473, 1482, 1578, 1623, 1797, 1953, 2028, 2142, 2238, 2370, 2772, 2868, 2973, 3033, 3393, 3483, 3582, 3777, 3822, 3840, 3912

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 05 2010

Keywords

• nonn

Comments

a(n) is necessarily a multiple of 3 for n > 1.

Examples

			3 = (2*1)^3/2 - 1 = prime(2), 3 + 2 = 5 = (2*1)^3/2 + 1, (3,5) is the first twin prime pair => a(1) = 1.
107 = (2*3)^3/2 - 1 = prime(28), 107 + 2 = 109 = (2*3)^3/2 + 1, (107,109) is the 10th twin prime pair => a(2) = 3.
		

Links

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

Crossrefs

Cf. A001359, A061308, A069496, A119859, A172271.

Programs

Mathematica

Select[Range[4000],AllTrue[(2#)^3/2+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 21 2015 *)

PARI

select(n -> isprime((2*n)^3/2-1) && isprime((2*n)^3/2+1), [1..4000]) \\ Satish Bysany, Mar 03 2017

Formula

2*a(n) = (2*A172271(n) + 2)^(1/3). - R. J. Mathar, Aug 21 2014