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

1,1

Comments

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

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A354813 A273201 A260730 * A279229 A339963 A141249

Adjacent sequences: A119970 A119971 A119972 * A119974 A119975 A119976

Keyword

easy,nonn

Author

Alford Arnold, Jun 03 2006

Extensions

More terms from Don Reble, Jul 24 2006

Status

approved