A071971 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.

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

Offset

1,2

Links

Table of n, a(n) for n=1..31.

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.

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}]

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, ", "))

Crossrefs

Cf. A071183.

Sequence in context: A134437 A018927 A001266 * A370253 A337553 A006680

Adjacent sequences: A071968 A071969 A071970 * A071972 A071973 A071974

Keyword

nonn

Author

Robert G. Wilson v, Jun 17 2002

Status

approved