OFFSET
1,1
COMMENTS
Necessarily p = 9 * (2*m - 1)^2 - 2.
REFERENCES
L. E. Dickson, History of the Theory of numbers, vol. 2: Diophantine Analysis, Dover Publications 2005.
H. Pieper, Zahlen aus Primzahlen. Eine Einfuehrung in die Zahlentheorie. VEB Deutscher Verlag der Wissenschaften, 2. Aufl., 1984.
A. Warusfel, Les nombres et leurs mystères, Edition du Seuil, Paris 1980.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
(7 + 11)/2 = 3^2, 1st term is prime(4) = 7.
(79 + 83)/2 = 9^2, 2nd term is prime(22) = 79.
m = 173 = prime(40): 21st term is p = 1071223 = prime(83637), p+2 = 3^4 * 5^2 * 23^2.
60th term is p = 27029599 = prime(1684797): p+2 = 3^2 * 1733^2.
MATHEMATICA
Select[Range[1617]^2 - 2, And @@ PrimeQ[# + {0, 4}] &] (* Amiram Eldar, Dec 24 2019 *)
PROG
(PARI) isok(n) = isprime(n) && isprime(n+4) && issquare(n+2) \\ Michel Marcus, Jul 22 2013
(PARI) forstep(n=3, 1e4, 2, if(isprime(n^2-2)&&isprime(n^2+2), print1(n^2-2", "))) \\ Charles R Greathouse IV, Jul 23 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 09 2010
EXTENSIONS
Edited by D. S. McNeil, Nov 18 2010
STATUS
approved