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

1,1

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)).

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A101731 A080765 A226039 * A234285 A314584 A335486

Adjacent sequences: A257289 A257290 A257291 * A257293 A257294 A257295

Keyword

nonn

Author

M. F. Hasler, May 08 2015

Status

approved