A257282 Numbers whose square is not the sum of two consecutive nonsquares.

0, 1, 2, 3, 4, 6, 7, 8, 10, 12, 14, 16, 17, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 41, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 99, 100, 102, 104, 106, 108, 110, 112, 114, 116

Offset: 1

Author

M. F. Hasler, May 08 2015

Keywords

• nonn
• easy

Comments

See A256944 for further information.

Union of even integers and A001333. - Ivan Neretin, Aug 04 2016

Examples

			5 is not in the sequence because 5^2 = 25 = 12 + 13 is the sum of two consecutive numbers both of which are not squares.
All even numbers are in the sequence because (2k)^2 = 4k^2 cannot be written as sum of two consecutive numbers and 2k^2 is not a square.
An odd number n is in the sequence if one of the two numbers next to n^2/2 is a square.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A256944.

Programs

Mathematica

Union[#, Range[0, Max@ #, 2]] &@ Numerator[Convergents[Sqrt@ 2, 7]] (* Michael De Vlieger, Aug 06 2016, after Harvey P. Dale at A001333 *)

PARI

is(n)={n%2==0 || issquare(n^2\2) || issquare(n^2\2+1)}

Formula

a(n) = sqrt(A256944).

a(n) ~ 2n. [Following Charles R Greathouse IV's formula for A256944.]