A119973 Numbers of the form (4k+1)*2^j which are not a sum of two squares.

21, 33, 42, 57, 66, 69, 77, 84, 93, 105, 114, 129, 132, 133, 138, 141, 154, 161, 165, 168, 177, 186, 189, 201, 209, 210, 213, 217, 228, 237, 249, 253, 258, 264, 266, 273, 276, 282, 285, 297, 301, 308, 309, 321, 322, 329, 330, 336, 341, 345, 354, 357, 372

Offset: 1

Author

Alford Arnold, Jun 03 2006

Keywords

• easy
• nonn

Comments

Intersection of A091072 and A022544. - Robert Israel, Oct 28 2018

Examples

			42 is there because it's (4*5+1)*2^1 and is not a sum of two squares.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001481, A022544, A084109, A091072, A120772.

Programs

Maple

filter:= proc(n) local w; w:= n/2^padic:-ordp(n,2);
w mod 4 = 1 and select(t -> t[2]::odd and t[1] mod 4 = 3, ifactors(w)[2]) <> []
end proc:
select(filter, [$1..1000]); # Robert Israel, Oct 28 2018

Mathematica

okQ[n_] := EvenQ[(n/2^IntegerExponent[n, 2]-1)/2] && SquaresR[2, n] == 0;
Select[Range[1000], okQ] (* Jean-François Alcover, Feb 09 2023 *)

Extensions

More terms from Don Reble, Jul 24 2006