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Squares of the form 2*p + 3, where p is a prime.
3

%I #14 Sep 07 2020 19:46:51

%S 9,25,49,121,169,361,529,625,841,961,1369,1681,2209,3025,4225,4489,

%T 5329,5929,6241,8281,9409,10201,10609,11881,14161,20449,22801,24025,

%U 24649,25921,34969,38809,42025,43681,44521,48841,51529,54289,55225,57121

%N Squares of the form 2*p + 3, where p is a prime.

%C The first seven terms are primes squared: 3^2, 5^2, 7^2, 11^2, 13^2, 17^2, 19^2, 23^2.

%H Charles R Greathouse IV, <a href="/A109367/b109367.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A109358(n)^2 = 2*A098828(n) + 3.

%t Select[Table[(2Prime[n] + 3)^(1/2), {n, 3500}], IntegerQ]^2 (* _Ray Chandler_, Aug 25 2005 *)

%t Select[2*Prime[Range[3500]]+3,IntegerQ[Sqrt[#]]&] (* _Harvey P. Dale_, Sep 07 2020 *)

%o (PARI) is(n)=issquare(n) && n%2 && isprime(n\2-1) \\ _Charles R Greathouse IV_, Aug 06 2013

%Y Cf. A098828, A109358.

%K nonn

%O 1,1

%A _Giovanni Teofilatto_, Aug 23 2005

%E Extended by _Ray Chandler_ and _Robert G. Wilson v_, Aug 25 2005