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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; text; 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

(PARI) is(n)=isprime(n^2-2)&&isprime(n^2+2) \\ Charles R Greathouse IV, Jul 02 2013

CROSSREFS

Cf. A028870, A028873, A038599, A153974.

Sequence in context: A071526 A114271 A137164 * A064539 A029482 A174786

Adjacent sequences:  A108698 A108699 A108700 * A108702 A108703 A108704

KEYWORD

nonn,easy

AUTHOR

John L. Drost, Jun 19 2005

STATUS

approved

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Last modified April 24 18:58 EDT 2014. Contains 240988 sequences.