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

1,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A302947 A326948 A159053 * A279131 A368620 A230670

Adjacent sequences: A172491 A172492 A172493 * A172495 A172496 A172497

Keyword

nonn

Author

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

Status

approved