|
| |
|
|
A108701
|
|
Values of n such that n^2-2 and n^2+2 are both prime.
|
|
13
| |
|
|
3, 9, 15, 21, 33, 117, 237, 273, 303, 309, 387, 429, 441, 447, 513, 561, 573, 609, 807, 897, 1035, 1071, 1113, 1143, 1233, 1239, 1311, 1563, 1611, 1617, 1737, 1749, 1827, 1839, 1953, 2133, 2211, 2283, 2589, 2715, 2721, 2955, 3081, 3093, 3453, 3549, 3555, 3621, 3807, 4305
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Since x^2+2 is divisible by 3 unless x is divisible by 3, all elements are 3 mod 6.
All values of n are members of A016945 (6n+3). - Gary Croft, Jul 06 2011
|
|
|
REFERENCES
| Beauregard, R.A. and Suryanarayan, E.R. Square-plus-two primes, Mathematical Gazette 85(502) 90-1
David Wells, Prime Numbers, John Wiley and Sons, 2005, p. 219 (article:'Siamese primes')
|
|
|
LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..8750
|
|
|
EXAMPLE
| 21 is on the list since 21^2-2=439 and 21^2+2=443 are primes.
|
|
|
MATHEMATICA
| a[n_]:=n^x-y; b[n_]:=n^x+y; lst={}; x=2; y=2; Do[If[PrimeQ[a[n]]&&PrimeQ[b[n]], AppendTo[lst, n]], {n, 0, 7!}]; lst [From Vladimir Orlovsky, Jan 03 2009]
|
|
|
PROG
| (MAGMA) [n: n in [3..3600 by 6] | IsPrime(n^2-2) and IsPrime(n^2+2)]; // Bruno Berselli, Apr 15 2011
|
|
|
CROSSREFS
| Cf. A028870, A028873, A038599, A153974 [From Vladimir Orlovsky, Jan 03 2009]
Sequence in context: A071526 A114271 A137164 * A064539 A029482 A174786
Adjacent sequences: A108698 A108699 A108700 * A108702 A108703 A108704
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| John L. Drost (drost(AT)marshall.edu), Jun 19 2005
|
| |
|
|
