OFFSET
1,2
COMMENTS
For k > 1: n = a(k) is necessarily a multiple of 3.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
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
KEYWORD
nonn
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 05 2010
STATUS
approved