

A183573


a(n) = n + floor(sqrt(2n+1)).


1



2, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92
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OFFSET

1,1


LINKS

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


FORMULA

From Robert Israel, Sep 12 2016: (Start)
a(n+1)=a(n)+2 if n is in A047838, otherwise a(n+1) = a(n)+1.
a(n) = n + A103128(n+1).
G.f.: Theta3(x^2)/(2*(1x)) + Theta2(x^2)/(2*sqrt(x)*(1x))  (12*x)*(3x)/(2*(1x)^2), where Theta2 and Theta3 are Jacobi Theta functions. (End)


MAPLE

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


MATHEMATICA

Table[n + Floor@ Sqrt[2 n + 1], {n, 80}] (* Michael De Vlieger, Sep 12 2016 *)


CROSSREFS

Cf. A047838, A103128, A116940 (complement).
Sequence in context: A035257 A235331 A175969 * A187895 A079726 A047498
Adjacent sequences: A183570 A183571 A183572 * A183574 A183575 A183576


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jan 05 2011


STATUS

approved



