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Search: id:A071183
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| A071183 |
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a(1)=1; a(n) is the smallest integer > a(n-1) such that the sum of elements of the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) equals n^2. |
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+0
3
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| 1, 3, 27, 51, 135, 138, 186, 187, 352, 479, 525, 923, 932, 1286, 1578, 1807, 1886, 1926, 2816, 3358, 3438, 5727, 50152, 156816, 204512, 213094, 221368, 255348, 257350, 329046, 403004, 434010, 442520, 449599, 450069, 452430, 457524, 459665
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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1/a(1)+1/a(2)+1/a(3)+1/a(4) = (1+1/3+1/27+1/51) which continued fraction is {1, 2, 1, 1, 3, 2, 1, 1, 4} and 1+2+1+1+3+2+1+1+4 = 16 = 4^2.
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = (s = Sum[1/a[i], {i, 1, n - 1}]; While[Plus @@ ContinuedFraction[s + 1/k] != n^2, k++ ]; k); k = 1; Do[ Print[ a[n]], {n, 1, 40}]
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PROGRAM
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(PARI) s=1; t=1; for(n=2, 40, s=s+1/t; while(abs(n^2+1-sum(i=1, length(contfrac(s+1/t)), component(contfrac(s+1/t), i)))>0, t++); print1(t, ", "))
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CROSSREFS
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Sequence in context: A108163 A108114 A147267 this_sequence A025414 A053360 A120117
Adjacent sequences: A071180 A071181 A071182 this_sequence A071184 A071185 A071186
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 10 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 17 2002
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