login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
OFFSET
1,1
LINKS
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*(1-x)) + Theta2(x^2)/(2*sqrt(x)*(1-x)) - (1-2*x)*(3-x)/(2*(1-x)^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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 05 2011
STATUS
approved