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A070899
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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 3n.
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0
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1, 6, 13, 16, 49, 71, 124, 188, 298, 326, 333, 354, 440, 797, 832, 954, 1006, 1040, 1280, 1319, 1414, 2038, 2113, 2231, 2291, 2924, 2973, 3107, 3983, 3984, 4331, 4605, 4763, 5756, 6314, 6325, 6402, 7501, 7967, 8073, 8143, 8895, 9567, 9900, 10333
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OFFSET
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1,2
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COMMENTS
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sum(k=>1,1/a(k))=C=1.3...
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LINKS
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EXAMPLE
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The continued fraction for S(7)=1+1/6+1/13+1/16+1/49+1/71+1/124 is [1, 2, 1, 6, 1, 1, 2, 3, 3, 1, 21, 1, 1, 3, 1, 3, 18, 3] where the largest element is 21=3*7 and 124 is the smallest integer > a(6)=71 with this property, hence a(7)=124.
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PROG
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(PARI) s=1; t=1; for(n=1, 60, s=s+1/t; while(abs(3*n-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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