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%I #6 Mar 30 2012 18:38:59
%S 1,2,7,15,16,23,50,60,72,123,149,164,166,185,236,494,495,569,589,654,
%T 802,951,968,1068,1178,1323,1356,1379,1399,1487,1946,2458,2500,2786,
%U 2911,3077,4282,4916,5156,5591,6047,6103,6639,7095,7786,8068,8493,9456
%N a(0)=1, a(n) is the smallest integer > a(n-1) such that the largest element in the simple continued fraction for S(n)= 1/a(0)+1/a(1)+1/a(2)+...+1/a(n) equals 2n.
%C sum(k=>1,1/a(k))=C=1.9...
%e The simple continued fraction for S(3)=1/a(0)+1/a(1)+1/a(2)+1/a(3)=1+1/2+1/7+1/15 is [1, 1, 2, 2, 3, 1, 6] where the largest element is 6=2*3. The simple continued fraction for 1+1/2+1/7+1/15+1/16 is [1, 1, 3, 2, 1, 1, 2, 2, 1, 8] where 8=2*4 is the largest element. Hence a(4)=16.
%o (PARI) s=1; t=1; for(n=1,60,s=s+1/t; while(abs(2*n-vecmax(contfrac(s+1/t)))>0,t++); print1(t,","))
%K easy,nonn
%O 0,2
%A _Benoit Cloitre_, May 19 2002
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