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

Author

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

Keywords

• nonn

Comments

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

Examples

			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, ...
		

Crossrefs

Cf. A338718, A338719.

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

Programs

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 *)