A109367 Squares of the form 2*p + 3, where p is a prime.

9, 25, 49, 121, 169, 361, 529, 625, 841, 961, 1369, 1681, 2209, 3025, 4225, 4489, 5329, 5929, 6241, 8281, 9409, 10201, 10609, 11881, 14161, 20449, 22801, 24025, 24649, 25921, 34969, 38809, 42025, 43681, 44521, 48841, 51529, 54289, 55225, 57121

Offset: 1

Author

Giovanni Teofilatto, Aug 23 2005

Keywords

• nonn

Comments

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A098828, A109358.

Programs

Mathematica

Select[Table[(2Prime[n] + 3)^(1/2), {n, 3500}], IntegerQ]^2 (* Ray Chandler, Aug 25 2005 *)
Select[2*Prime[Range[3500]]+3,IntegerQ[Sqrt[#]]&] (* Harvey P. Dale, Sep 07 2020 *)

PARI

is(n)=issquare(n) && n%2 && isprime(n\2-1) \\ Charles R Greathouse IV, Aug 06 2013

Formula

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

Extensions

Extended by Ray Chandler and Robert G. Wilson v, Aug 25 2005