

A108701


Values of n such that n^22 and n^2+2 are both prime.


14



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, 3723, 3807
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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.
Intersection of A067201 and A028870.  Robert Israel, Sep 11 2014


REFERENCES

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
Raymond A. Beauregard and E. R. Suryanarayan, Squareplustwo primes, Mathematical Gazette 85(502) 901.


EXAMPLE

21 is on the list since 21^2  2 = 439 and 21^2 + 2 = 443 are primes.


MAPLE

select(n > isprime(n^22) and isprime(n^2+2), [seq(6*i+3, i=0..1000)]); # Robert Israel, Sep 11 2014


MATHEMATICA

Select[Range[5000], PrimeQ[#^2  2] && PrimeQ[#^2 + 2] &] (* Alonso del Arte, Sep 11 2014 *)


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

Subsequence of A016945.
Cf. A016945, A028870, A028873, A038599, A067201, 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


EXTENSIONS

Terms corrected by Charles R Greathouse IV, Sep 11 2014


STATUS

approved



