

A103128


n appears 2 * ceiling(n/2) times.


6



1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12
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OFFSET

1,3


LINKS

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


FORMULA

a(n) = floor(sqrt(2n1)).
From Robert Israel, Sep 12 2016: (Start)
a(n+1) = a(n)+1 for n in A007590, otherwise a(n+1) = a(n).
G.f.: x*Theta3(x^2)/(2*(1x)) + sqrt(x)*Theta2(x^2)/(2*(1x))  x/(2*(1x)), where Theta2 and Theta3 are Jacobi Theta functions. (End)


MAPLE

seq(floor(sqrt(2*n1)), n=1..100); # Robert Israel, Sep 12 2016


MATHEMATICA

Table[Floor[Sqrt[2n1]], {n, 1, 100}] (* Mohammad K. Azarian, Jun 15 2016 *)


PROG

(Haskell)
a103128 = a000196 . (subtract 1) . (* 2)
 Reinhard Zumkeller, Feb 12 2012


CROSSREFS

Cf. A172471, A000196, A005408, A007590.
Sequence in context: A071626 A182008 A106457 * A156080 A271058 A107320
Adjacent sequences: A103125 A103126 A103127 * A103129 A103130 A103131


KEYWORD

easy,nonn


AUTHOR

Giovanni Teofilatto, Mar 17 2005


EXTENSIONS

Edited by Franklin T. AdamsWatters, Apr 20 2010


STATUS

approved



