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a(0)=1. a(n+1) = a(ceiling(n/a(n))) + 1.
2

%I #15 May 15 2017 23:11:44

%S 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 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 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 a(0)=1. a(n+1) = a(ceiling(n/a(n))) + 1.

%C 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 N. J. A. Sloane, <a href="/A130193/b130193.txt">Table of n, a(n) for n = 0..20000</a>

%p A130193 := proc(n)

%p option remember;

%p if n = 0 then

%p 1;

%p else

%p 1+procname(ceil((n-1)/procname(n-1))) ;

%p end if;

%p end proc:

%p seq(A130193(n),n=0..50) ; # _R. J. Mathar_, Sep 10 2015

%Y Cf. A094294, A130147.

%K easy,nonn

%O 0,2

%A _Leroy Quet_, Aug 05 2007