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A183300 Positive integers not of the form 2n^2. 2
1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Complement of A001105.

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

EXAMPLE

10 is in the sequence since 2*2^2=8 < 10 < 2*3^2=18.

MAPLE

A183300:=n->if type(sqrt(2*n)/2, integer) then NULL; else n; fi; seq(A183300(n), n=1..100); # Wesley Ivan Hurt, Dec 17 2013

MATHEMATICA

a = 2; b = 0;

F[n_] := a*n^2 + b*n;

R[n_] := (n/a + ((b - 1)/(2a))^2)^(1/2);

G[n_] := n - 1 + Ceiling[R[n] - (b - 1)/(2a)];

Table[F[n], {n, 60}]

Table[G[n], {n, 100}] (* Clark Kimberling *)

r[n_] := Reduce[n == 2*k^2, k, Integers]; Select[Range[100], r[#] === False &] (* Jean-Fran├žois Alcover, Dec 17 2013 *)

max = 100; Complement[Range[max], 2 Range[Ceiling[Sqrt[max/2]]]^2] (* Alonso del Arte, Dec 17 2013 *)

PROG

(MAGMA) [n: n in [0..100] | not IsSquare(n/2)]; // Bruno Berselli, Dec 17 2013

(PARI) is(n)=!issquare(n/2) \\ Charles R Greathouse IV, Sep 02 2015

(PARI) a(n)=my(k=sqrtint(n\2)+n); if(k-sqrtint(k\2)<n, k+1, k) \\ Charles R Greathouse IV, Sep 02 2015

CROSSREFS

Cf. A001105.

Sequence in context: A210934 A194276 A184336 * A155854 A047252 A039235

Adjacent sequences:  A183297 A183298 A183299 * A183301 A183302 A183303

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jan 03 2011

EXTENSIONS

Name clarified by Wesley Ivan Hurt, Dec 17 2013

STATUS

approved

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Last modified April 21 23:52 EDT 2021. Contains 343156 sequences. (Running on oeis4.)