login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A176130 Lesser of a pair (p,p+4) of cousin primes whose arithmetic mean p+2 is a square number. 5
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 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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 4 01:43 EDT 2020. Contains 336201 sequences. (Running on oeis4.)