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a(1)=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(1)+1/a(2)+...+1/a(n) equals n^2.
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%I #6 Mar 30 2012 18:38:59

%S 1,4,14,19,25,282,393,415,460,501,1839,2835,3422,4718,4909,6350,6678,

%T 11087,12941,16503,16568,21585,24446,31506,35164,35380,40323,46001,

%U 46905,52205,56210,56441,60038,92562,97354,101710,102136,107680,127299

%N a(1)=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(1)+1/a(2)+...+1/a(n) equals n^2.

%C sum(k=>1,1/a(k))=C=1.429...

%e The continued fraction for S(6)=1+1/4+1/14+1/19+1/25+1/282 is [1, 2, 2, 1, 1, 6, 1, 4, 5, 36, 1, 3, 2, 2] where the largest element is 36=6^2 and 282 is the smallest integer > 25 with this property.

%o (PARI) s=1; t=1; for(n=2,47,s=s+1/t; while(abs(n^2-vecmax(contfrac(s+1/t)))>0,t++); print1(t,","))

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, May 19 2002