A338720 Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = nearest integer to b(n).

1, 2, 2, 3, 2, 3, 2, 4, 2, 4, 3, 4, 3, 5, 3, 5, 3, 5, 4, 6, 4, 6, 4, 6, 4, 6, 4, 7, 4, 7, 4, 7, 5, 7, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 9, 5, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 7, 10, 7, 11, 7, 11, 7, 11, 7, 11, 7, 11, 7, 11, 7, 11, 7, 12, 7, 12, 7

Offset

1,2

Comments

Since b(3) = 3/2, a(3) could also be taken to be 1.

Links

Table of n, a(n) for n=1..87.

Example

The first few fractions b(n) are 1, 2, 3/2, 8/3, 15/8, 16/5, 35/16, 128/35, 315/128, 256/63, 693/256, 1024/231, 3003/1024, 2048/429, ...

Maple

A338720b := proc(n)
    option remember ;
    if n = 1 then
        1;
    else
        n/procname(n-1) ;
    end if;
end proc:
A338720 := proc(n)
    round(A338720b(n)) ;
end proc:
seq(A338720(n), n=1..87) ; # R. J. Mathar, Dec 01 2020

Mathematica

b[n_] := b[n] = If[n == 1, 1, n/b[n-1]];
a[n_] := Round[b[n]];
Table[a[n], {n, 1, 87}] (* Jean-François Alcover, Apr 23 2023 *)

Crossrefs

Cf. A338718, A338719.

For the numerators and denominators of b(n) see A004731 and A004730.

Sequence in context: A052180 A065151 A345874 * A320013 A299990 A175193

Adjacent sequences: A338717 A338718 A338719 * A338721 A338722 A338723

Keyword

nonn

Author

N. J. A. Sloane, Nov 29 2020, following a suggestion from Anchar Koops, Nov 24 2020

Status

approved