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URL: https://oeis.org/A172494

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A172494
Numbers k with (p,p+2) = ((2*k)^3/2 - 1,(2*k)^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
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
KEYWORD
nonn
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 05 2010
STATUS
approved