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A071971
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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^3.
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0
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1, 7, 45, 401, 719, 1136, 5613, 6358, 12448, 24739, 28082, 42850, 59604, 78928, 81119, 169213, 214725, 309015, 432821, 496399, 706170, 725188, 1163780, 2284457, 2941839, 3857806, 4133465, 5890433, 6190258, 6286719, 6888119
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| 1/a(1)+1/a(2)+1/a(3)+1/a(4) = (1+1/7+1/45+1/401) which continued fraction is {1, 5, 1, 29, 1, 4, 3, 1, 1, 18} and 1+5+1+29+1+4+3+1+1+18 = 64 = 4^3.
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MATHEMATICA
| a[1] = 1; a[n_] := a[n] = (s = Sum[1/a[i], {i, 1, n - 1}]; While[Plus @@ ContinuedFraction[s + 1/k] != n^3, k++ ]; k); k = 1; Do[ Print[ a[n]], {n, 1, 31}]
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PROG
| (PARI) s=1; t=1; for(n=2, 31, s=s+1/t; while(abs(n^3+1-sum(i=1, length(contfrac(s+1/t)), component(contfrac(s+1/t), i)))>0, t++); print1(t, ", "))
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CROSSREFS
| Cf. A071183.
Sequence in context: A134437 A018927 A001266 * A006680 A197796 A197856
Adjacent sequences: A071968 A071969 A071970 * A071972 A071973 A071974
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 17 2002
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