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A176130 Lesser of a pair (p,p+4) of cousin primes whose arithmetic mean p+2 is a square number. 4
7, 79, 223, 439, 1087, 13687, 56167, 74527, 91807, 95479, 149767, 184039, 194479, 199807, 263167, 314719, 328327, 370879, 651247, 804607, 1071223, 1147039, 1238767, 1306447, 1520287, 1535119, 1718719, 2442967, 2595319, 2614687 (list; graph; refs; listen; history; text; internal format)
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 mysteres, Edition du Seuil, Paris 1980

LINKS

Table of n, a(n) for n=1..30.

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.

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

Cf. A023200, A046132, A174454.

Sequence in context: A023285 A135051 A201860 * A014232 A154592 A075896

Adjacent sequences:  A176127 A176128 A176129 * A176131 A176132 A176133

KEYWORD

nonn

AUTHOR

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 09 2010

EXTENSIONS

Edited by D. S. McNeil, Nov 18 2010

STATUS

approved

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Last modified July 15 20:23 EDT 2019. Contains 325056 sequences. (Running on oeis4.)