A338720 - OEIS

%I #15 Apr 23 2023 12:18:14

%S 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,

%T 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,

%U 7,10,7,11,7,11,7,11,7,11,7,11,7,11,7,11,7,12,7,12,7

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

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

%e 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, ...

%p A338720b := proc(n)

%p     option remember ;

%p     if n = 1 then

%p         1;

%p     else

%p         n/procname(n-1) ;

%p     end if;

%p end proc:

%p A338720 := proc(n)

%p     round(A338720b(n)) ;

%p end proc:

%p seq(A338720(n),n=1..87) ; # _R. J. Mathar_, Dec 01 2020

%t b[n_] := b[n] = If[n == 1, 1, n/b[n-1]];

%t a[n_] := Round[b[n]];

%t Table[a[n], {n, 1, 87}] (* _Jean-François Alcover_, Apr 23 2023 *)

%Y Cf. A338718, A338719.

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

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Nov 29 2020, following a suggestion from _Anchar Koops_, Nov 24 2020