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A130193 a(0)=1. a(n+1) = a(ceiling(n/a(n))) + 1.

%I A130193 #15 May 15 2017 23:11:44
%S A130193 1,2,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,4,5,4,5,5,5,5,5,5,5,5,5,5,5,5,
%T A130193 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%U A130193 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,5,6,5,6,5,5
%N A130193 a(0)=1. a(n+1) = a(ceiling(n/a(n))) + 1.
%C A130193 Records 1,2,3,4,5,... appear at n = 0, 1, 2, 5, 18, 87, 518, 3621,.. which appears to be essentially A094294. - _R. J. Mathar_, Sep 10 2015
%H A130193 N. J. A. Sloane, <a href="/A130193/b130193.txt">Table of n, a(n) for n = 0..20000</a>
%p A130193 A130193 := proc(n)
%p A130193     option remember;
%p A130193     if n = 0 then
%p A130193         1;
%p A130193     else
%p A130193         1+procname(ceil((n-1)/procname(n-1))) ;
%p A130193     end if;
%p A130193 end proc:
%p A130193 seq(A130193(n),n=0..50) ; # _R. J. Mathar_, Sep 10 2015
%Y A130193 Cf. A094294, A130147.
%K A130193 easy,nonn
%O A130193 0,2
%A A130193 _Leroy Quet_, Aug 05 2007