OFFSET
1,1
COMMENTS
First differences are 4 and 5. Also, there is no immediate pattern in parity of a(n).
Are similar sequences well defined (in terms of rounding problems)? See also A086843, A086844, A196468.
Answer: I would not call the sequences A086843, A086844, A196468 'similar' to (a(n)). The first differences d =5,5,5,5,4,5,5,5,5,4,... are a Sturmian sequence (d(n)) with slope alpha = 2 + sqrt(8) and intercept 0. We give d offset 0 by setting d(0):=4. By Hofstadter's Fundamental Theorem of eta-sequences, the chunks 45555 and 455555 occur following a Sturmian sequence with density beta = (sqrt(8) - 2)/(3 - sqrt(8)). Since beta = 2 + sqrt(8) = alpha, the sequence (d(n)) is fixed point of the substitution 4->45555, 5->455555. See A197879 for a complete description of the parity pattern of (a(n)). - Michel Dekking, Jan 24 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, 2012; J. Int. Seq. 16 (2013) #13.1.8
D. R. Hofstadter, Eta-Lore [Cached copy, with permission]
N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)
FORMULA
a(n) = A003151(2n). - R. J. Mathar, Oct 20 2011
MATHEMATICA
Table[Floor[((2+Sqrt[8]))*n], {n, 100}]
PROG
(PARI) a(n)=2*n+sqrtint(8*n^2) \\ Charles R Greathouse IV, Oct 25 2011
(Magma) [Floor(2*(1 + Sqrt(2))*n): n in [1..100]]; // G. C. Greubel, Aug 18 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Oct 18 2011
STATUS
approved