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A172494 Numbers n with (p,p+2) = ((2*n)^3/2 - 1,(2*n)^3/2 + 1) is a twin prime pair. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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

Sequence in context: A302947 A326948 A159053 * A279131 A230670 A232069

Adjacent sequences:  A172491 A172492 A172493 * A172495 A172496 A172497

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 21 06:25 EDT 2019. Contains 328292 sequences. (Running on oeis4.)