A257292 Numbers whose square can be written as the sum of two consecutive nonsquares.

5, 9, 11, 13, 15, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131

Offset: 1

Author

M. F. Hasler, May 08 2015

Keywords

• nonn

Comments

Equivalently, odd numbers such that neither of the two integers next to n^2/2 is a square.

Complement of A257282 = square roots of A256944.

The odd numbers missing here are 1, 3, 7, 17, 41, 99, ... = A078057 (see also A001333 = abs(A123335)).

Examples

			9 is a term because 9^2 = 81 = 40 + 41, neither of which are square.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001333, A078057, A123335, A256944, A257282.

Programs

Mathematica

Select[Range[1, 131, 2], AllTrue[{Floor[#^2/2], Ceiling[#^2/2]}, ! IntegerQ@ Sqrt@ # &] &] (* Michael De Vlieger, Dec 11 2015 *)

PARI

select( is(n)={bittest(n,0) && !issquare(n^2\2) && !issquare(n^2\/2)}, [0..140]) \\ Corrected Jul 06 2021, thanks to an observation by Bill McEachen