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A070900
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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 the number of elements in this continued fraction.
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0
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1, 2, 4, 10, 32, 44, 47, 56, 61, 249, 261, 379, 410, 418, 418, 457, 554, 576, 938, 1262, 1524, 1636, 1813, 1817, 1849, 1851, 1914, 2127, 2192, 2243, 2345, 2413, 2511, 2579, 2722, 2777, 2939, 3002, 3309, 3361, 3504, 4178, 4404, 4911, 6088, 8623, 9104, 9468
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OFFSET
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0,2
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COMMENTS
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sum(k=>0,1/a(k))=C=1.99...
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LINKS
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Table of n, a(n) for n=0..47.
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EXAMPLE
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The continued fraction for S(11)=1+1/2+1/4+1/10+1/32+1/44+1/47+1/56+1/61+1/249+1/261+1/379 is [1, 1, 32, 3, 10, 6, 1, 1, 1, 8, 1, 1, 1, 1, 2, 1, 9, 3, 1, 1, 2, 23, 3, 1, 1, 2, 1, 21, 1, 1, 5, 3] which contains 32 elements and with largest element 32.
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PROG
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(PARI) s=1; t=1; for(n=1, 60, s=s+1/t; while(abs(length(contfrac(s+1/t))-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))
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CROSSREFS
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Sequence in context: A005268 A243931 A005269 * A296003 A263662 A151400
Adjacent sequences: A070897 A070898 A070899 * A070901 A070902 A070903
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre, May 19 2002
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STATUS
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approved
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