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A049068 Complement of quarter-squares (A002620). 8
3, 5, 7, 8, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A000037 and A078358. - Reinhard Zumkeller, May 08 2012

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = n + A027434(n).

Other identities and observations. For all n >= 1:

A237347(a(n)) = 2. - Reinhard Zumkeller, Mar 18 2014

A240025(a(n)) = 0. - Reinhard Zumkeller, Jul 05 2014

a(n) = A080037(n) - 1. - Peter Kagey, Dec 08 2015

G.f.: x/(1-x)^2 + Sum_{k>=0} (x^(1+k^2)*(1+x^k))/(1-x)

= (x*Theta3(x)+ x^(3/4)*Theta2(x))/(2-2*x) + (3-x)*x/(2*(1-x)^2) where Theta3 and Theta2 are Jacobi Theta functions. - Robert Israel, Dec 09 2015

MAPLE

A049068:=n->n + ceil(2*sqrt(n)); seq(A049068(n), n=1..100); # Wesley Ivan Hurt, Mar 01 2014

MATHEMATICA

max = 100; Complement[Range[0, max], Table[Quotient[n^2, 4], {n, 0, 2*Sqrt[max]}]]  (* Jean-Fran├žois Alcover, Apr 18 2013 *)

Table[n + Ceiling[2 * Sqrt[n]], {n, 100}] (* Wesley Ivan Hurt, Mar 01 2014 *)

PROG

(PARI) {a(n) = if( n<1, 0, n+1 + sqrtint(4*n - 3))} /* Michael Somos, Oct 16 2006 */

(Haskell)

a049068 n = a049068_list !! (n-1)

a049068 = filter ((== 0) . a240025) [0..]

-- Reinhard Zumkeller, Jul 05 2014, Mar 18 2014, May 08 2012

(MAGMA) [n+Ceiling(2*Sqrt(n)): n in [1..70]]; // Vincenzo Librandi, Dec 09 2015

CROSSREFS

Complement: A002620.

Cf. A000037, A027434, A078358, A080037, A237347, A240025.

Sequence in context: A189829 A175146 A171508 * A185602 A225554 A257019

Adjacent sequences:  A049065 A049066 A049067 * A049069 A049070 A049071

KEYWORD

nonn,nice,easy,changed

AUTHOR

Michael Somos, Aug 06 1999

STATUS

approved

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.