A337723 a(n) = prime(n-2) - ceiling(a(n-2)/2); a(1)=0, a(2)=1.

0, 1, 2, 2, 4, 6, 9, 10, 12, 14, 17, 22, 22, 26, 30, 30, 32, 38, 43, 42, 45, 50, 50, 54, 58, 62, 68, 70, 69, 72, 74, 77, 90, 92, 92, 93, 103, 104, 105, 111, 114, 117, 122, 122, 130, 132, 132, 133, 145, 156, 154, 151, 156, 163, 163, 169, 175, 178, 181, 182, 186, 190, 190

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(3) = prime(1) - ceiling(a(1)/2) =  2 - ceiling(0/2) = 2,
a(4) = prime(2) - ceiling(a(2)/2) =  3 - ceiling(1/2) = 2,
a(5) = prime(3) - ceiling(a(3)/2) =  5 - ceiling(2/2) = 4,
a(6) = prime(4) - ceiling(a(4)/2) =  7 - ceiling(2/2) = 6,
a(7) = prime(5) - ceiling(a(5)/2) = 11 - ceiling(4/2) = 9.

Mathematica

a[1] = 0; a[2] = 1; a[n_] := a[n] = Floor[(2*Prime[n - 2] - a[n - 2])/2]; Array[a, 100] (* Amiram Eldar, Sep 18 2020 *)
nxt[{n_, a_, b_}]:={n+1, b, Prime[n-1]-Ceiling[a/2]}; Join[{0, 1, 2}, Drop[NestList[nxt, {3, 2, 2}, 70][[All, 2]], 2]] (* Harvey P. Dale, May 13 2022 *)

Prog

(Ruby) require 'prime'
values = [0, 1]
Prime.each(100) do |prime|
    values << prime - (values[-2]+1) / 2
end
p values
(PARI) a(n) = if (n<=2, n-1, prime(n-2) - ceil(a(n-2)/2)); \\ Michel Marcus, Oct 07 2020

Crossrefs

Cf. A000040. Similar to A337724 with ceiling instead of floor.

Sequence in context: A091966 A231187 A055529 * A222735 A299408 A338937

Adjacent sequences: A337720 A337721 A337722 * A337724 A337725 A337726

Keyword

nonn

Author

Simon Strandgaard, Sep 17 2020

Status

approved