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A338719 Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = ceiling(b(n)).

%I A338719 #14 Jul 22 2024 15:25:45
%S A338719 1,2,2,3,2,4,3,4,3,5,3,5,3,5,4,6,4,6,4,6,4,6,4,7,5,7,5,7,5,7,5,8,5,8,
%T A338719 5,8,5,8,6,8,6,9,6,9,6,9,6,9,6,9,6,10,6,10,6,10,7,10,7,10,7,10,7,11,7,
%U A338719 11,7,11,7,11,7,11,7,11,7,11,8,12,8,12,8,12,8,12,8,12,8
%N A338719 Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = ceiling(b(n)).
%H A338719 Robert Israel, <a href="/A338719/b338719.txt">Table of n, a(n) for n = 1..10000</a>
%e A338719 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 A338719 R:= 1:
%p A338719 b:= 1:
%p A338719 for i from 2 to 100 do
%p A338719   b:= i/b;
%p A338719   R:= R, ceil(b)
%p A338719 od:
%p A338719 R; # _Robert Israel_, Jul 21 2024
%Y A338719 Cf. A338718, A338720.
%Y A338719 For the numerators and denominators of b(n) see A004731 and A004730.
%K A338719 nonn,look
%O A338719 1,2
%A A338719 _N. J. A. Sloane_, Nov 29 2020, following a suggestion from _Anchar Koops_, Nov 24 2020