OFFSET
1,2
COMMENTS
I conjecture that infinitely many terms are prime. For n<=10^5, exactly 5115 terms are prime. For n<=10^7, there are 352704 prime terms. The largest prime for n<10^10 is at n=9999999983, a(n)=16666666618226308891. Below 10^100, n=(10^100)-345. Below 10^500, n=(10^500)-2414. - Griffin N. Macris, May 04 2016
Since (n^2+3n)/6 < a(n) < (n^2+5n+4)/6, the sum of reciprocals of this sequence converges to a value between 13/6 and 11/3, approximately 2.888. - Griffin N. Macris, May 07 2016
FORMULA
From Griffin N. Macris, May 04 2016 (Start)
a(0) = 0; a(n) = A000217(ceiling(n/2)) + a(floor(n/2)).
Asymptotically, a(n) ~ (n^2+3n)/6. (End)
a(n) = (A135013(n) + n)/2. - Amiram Eldar, Dec 27 2022
MATHEMATICA
a[0]:=0;
a[n_]:=Ceiling[n/2](1+Ceiling[n/2])/2 + a[Floor[n/2]];
Array[a, 50] (* Griffin N. Macris, May 04 2016 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Jonathan Vos Post, Apr 03 2010
STATUS
approved