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

1,3

Comments

See A256944 for further information.

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

Links

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

Formula

a(n) = sqrt(A256944).

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A256944.

Sequence in context: A225620 A335041 A335042 * A336488 A221178 A080389

Adjacent sequences: A257279 A257280 A257281 * A257283 A257284 A257285

Keyword

nonn,easy

Author

M. F. Hasler, May 08 2015

Status

approved