

A108701


Values of n such that n^22 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
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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. Squareplustwo primes, Mathematical Gazette 85(502) 901
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 21^22=439 and 21^2+2=443 are primes.


MATHEMATICA

a[n_]:=n^xy; 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^22) and IsPrime(n^2+2)]; // Bruno Berselli, Apr 15 2011
(PARI) is(n)=isprime(n^22)&&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



