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A071012
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a(1)=1, a(n) is the smallest number > a(n-1) such that the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) contains exactly n elements.
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1
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1, 2, 3, 11, 16, 21, 27, 35, 42, 51, 55, 63, 75, 89, 350, 364, 385, 385, 416, 450, 453, 468, 476, 483, 526, 604, 617, 780, 1125, 1157, 1263, 1935, 7000, 7028, 7774, 8928, 9378, 62628, 865117
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..39.
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EXAMPLE
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The continued fraction for S(6)=1+1/2+1/3+1/11+1/16+1/21 is [2, 29, 9, 1, 3, 3] which contains 6 elements. The continued fraction for 1+1/2+1/3+1/11+1/16+1/21+1/27 is [2, 14, 169, 1, 1, 1, 4] which contains 7 elements and 27 is the smallest number >21 with this property, hence a(7)=27.
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PROG
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(PARI) s=1; t=1; for(n=1, 38, s=s+1/t; while(abs(n-length(contfrac(s+1/t)))>0, t++); print1(t, ", "))
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CROSSREFS
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Sequence in context: A144979 A194558 A076514 * A091734 A038902 A019355
Adjacent sequences: A071009 A071010 A071011 * A071013 A071014 A071015
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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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EXTENSIONS
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One more term from Thomas Baruchel (baruchel(AT)users.sourceforge.net), Nov 16 2003
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STATUS
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approved
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