cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A176130 Lesser of a pair (p,p+4) of cousin primes whose arithmetic mean p+2 is a square number.

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%I A176130 #19 Dec 24 2019 08:29:41
%S A176130 7,79,223,439,1087,13687,56167,74527,91807,95479,149767,184039,194479,
%T A176130 199807,263167,314719,328327,370879,651247,804607,1071223,1147039,
%U A176130 1238767,1306447,1520287,1535119,1718719,2442967,2595319,2614687
%N A176130 Lesser of a pair (p,p+4) of cousin primes whose arithmetic mean p+2 is a square number.
%C A176130 Necessarily p = 9 * (2*m - 1)^2 - 2.
%D A176130 L. E. Dickson, History of the Theory of numbers, vol. 2: Diophantine Analysis, Dover Publications 2005.
%D A176130 H. Pieper, Zahlen aus Primzahlen. Eine Einfuehrung in die Zahlentheorie. VEB Deutscher Verlag der Wissenschaften, 2. Aufl., 1984.
%D A176130 A. Warusfel, Les nombres et leurs mystères, Edition du Seuil, Paris 1980.
%H A176130 Amiram Eldar, <a href="/A176130/b176130.txt">Table of n, a(n) for n = 1..10000</a>
%e A176130 (7 + 11)/2 = 3^2, 1st term is prime(4) = 7.
%e A176130 (79 + 83)/2 = 9^2, 2nd term is prime(22) = 79.
%e A176130 m = 173 = prime(40): 21st term is p = 1071223 = prime(83637), p+2 = 3^4 * 5^2 * 23^2.
%e A176130 60th term is p = 27029599 = prime(1684797): p+2 = 3^2 * 1733^2.
%t A176130 Select[Range[1617]^2 - 2, And @@ PrimeQ[# + {0, 4}] &] (* _Amiram Eldar_, Dec 24 2019 *)
%o A176130 (PARI) isok(n) = isprime(n) && isprime(n+4) && issquare(n+2) \\ _Michel Marcus_, Jul 22 2013
%o A176130 (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
%Y A176130 Cf. A023200, A046132, A174454.
%K A176130 nonn
%O A176130 1,1
%A A176130 Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 09 2010
%E A176130 Edited by _D. S. McNeil_, Nov 18 2010