cp's OEIS Frontend

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

%I A338720 #15 Apr 23 2023 12:18:14
%S A338720 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 A338720 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 A338720 7,10,7,11,7,11,7,11,7,11,7,11,7,11,7,11,7,12,7,12,7
%N A338720 Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = nearest integer to b(n).
%C A338720 Since b(3) = 3/2, a(3) could also be taken to be 1.
%e A338720 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 A338720 A338720b := proc(n)
%p A338720     option remember ;
%p A338720     if n = 1 then
%p A338720         1;
%p A338720     else
%p A338720         n/procname(n-1) ;
%p A338720     end if;
%p A338720 end proc:
%p A338720 A338720 := proc(n)
%p A338720     round(A338720b(n)) ;
%p A338720 end proc:
%p A338720 seq(A338720(n),n=1..87) ; # _R. J. Mathar_, Dec 01 2020
%t A338720 b[n_] := b[n] = If[n == 1, 1, n/b[n-1]];
%t A338720 a[n_] := Round[b[n]];
%t A338720 Table[a[n], {n, 1, 87}] (* _Jean-François Alcover_, Apr 23 2023 *)
%Y A338720 Cf. A338718, A338719.
%Y A338720 For the numerators and denominators of b(n) see A004731 and A004730.
%K A338720 nonn
%O A338720 1,2
%A A338720 _N. J. A. Sloane_, Nov 29 2020, following a suggestion from _Anchar Koops_, Nov 24 2020