A073098 - OEIS

%I #9 Nov 17 2024 13:55:09

%S 2,3,11,2,5,6,13,17,6,2,7,11,23,18,3,8,2,73,7,31,2,22,201,71,19,29,23,

%T 19,139,59,37,43,15,263,17,131,71,16,257,6,227,363,191,83,16,113,123,

%U 234,178,457,197,106,38,8,208,173,29,895,515,313,162,808,1996,622,274

%N a(1)=2, a(n) is the smallest positive integer such that the continued fraction for 1/a(1)+1/a(2)+....+1/a(n) contains strictly more elements than the continued fraction for 1/a(1)+1/a(2)+....+1/a(n-1).

%H Sean A. Irvine, <a href="/A073098/b073098.txt">Table of n, a(n) for n = 1..233</a>

%e The continued fraction for 1/a(1)+1/a(2)+1/a(3)+1/a(4) is [1, 2, 2, 1, 4] with 5 elements. The continued fraction for (1/2+1/3+1/11+1/2+1/5) is [1, 1, 1, 1, 1, 1, 20] which contains 7 elements and 5 is the smallest integer with this property, hence a(5)=5.

%K nonn,changed

%O 1,1

%A _Benoit Cloitre_, Aug 18 2002