A281898 Numbers n such that n - floor(sqrt(n))^2 and 2n - floor(sqrt(2n))^2 are both squares.

0, 1, 2, 4, 5, 8, 10, 13, 17, 20, 25, 29, 34, 40, 45, 50, 58, 65, 80, 85, 97, 100, 125, 130, 145, 170, 185, 200, 221, 225, 250, 260, 265, 290, 325, 340, 365, 377, 400, 425, 445, 450, 485, 493, 520, 530, 545, 580, 625, 650, 680, 685, 730, 754, 765, 785, 800, 841, 845, 890, 900

Offset

1,3

Comments

The sequence is infinite: it contains an infinite subsequence { A000129(2*k)^2 + 1, k>=0 }. - Max Alekseyev, Feb 01 2017

Also A000129(2k+1)^2 is a subsequence.

There are precisely six primes in this sequence: 2, 5, 13, 17, 29, and 97.

Links

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

Mathematica

Select[Range[0, 900], Times @@ Boole@ Map[IntegerQ@ Sqrt@ # &, # - Floor[Sqrt@ #]^2 &@ {#, 2 #}] == 1 &] (* Michael De Vlieger, Feb 02 2017 *)
Select[Range[0, 1000], AllTrue[{Sqrt[#-Floor[Sqrt[#]]^2], Sqrt[2#-Floor[ Sqrt[ 2#]]^2]}, IntegerQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 25 2020 *)

Prog

(PARI) is(n)=issquare(n-sqrtint(n)^2) && issquare(2*n-sqrtint(2*n)^2) \\ Charles R Greathouse IV, Feb 01 2017

Crossrefs

Cf. A000129, A076218 is a subsequence, A145016.

Sequence in context: A126026 A199425 A057129 * A036404 A347355 A186077

Adjacent sequences: A281895 A281896 A281897 * A281899 A281900 A281901

Keyword

nonn

Author

Thomas Ordowski, Feb 01 2017

Extensions

More terms from Altug Alkan, Feb 01 2017

Status

approved