A088462 a(1)=1, a(n) = ceiling((n - a(a(n-1)))/2).

1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30, 30, 31, 31, 32, 32

Offset

1,4

Comments

Partial sums of A004641. - Reinhard Zumkeller, Dec 05 2009

This sequence generates A004641; see comment at A004641. - Clark Kimberling, May 25 2011

Links

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

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Formula

a(n) = floor((sqrt(2)-1)*n + 1/sqrt(2)).

a(1) = a(2) = 1; a(n) = n - a(n-1) - a(a(n-2)) for n > 2. - Altug Alkan, Jun 24 2017

Mathematica

Table[Floor[(Sqrt[2] - 1) n + 1 / Sqrt[2]], {n, 100}] (* Vincenzo Librandi, Jun 26 2017 *)

Prog

(Python)
l=[0, 1, 1]
for n in range(3, 101): l.append(n - l[n - 1] - l[l[n - 2]])
print(l[1:]) # Indranil Ghosh, Jun 24 2017, after Altug Alkan
(Magma) [Floor((Sqrt(2)-1)*n+1/Sqrt(2)): n in [1..100]]; // Vincenzo Librandi, Jun 26 2017

Crossrefs

Cf. A005206.

The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A000201 as the parent: A000201, A001030, A001468, A001950, A003622, A003842, A003849, A004641, A005614, A014675, A022342, A088462, A096270, A114986, A124841. - N. J. A. Sloane, Mar 11 2021

Sequence in context: A331535 A248170 A225545 * A189574 A233795 A093337

Adjacent sequences: A088459 A088460 A088461 * A088463 A088464 A088465

Keyword

nonn

Author

Benoit Cloitre, Nov 12 2003

Status

approved