A070903 a(1)=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(1)+1/a(2)+...+1/a(n) equals n^3.

1, 8, 1784, 2322, 2781, 6133, 6619, 12814, 15199, 54262, 70863, 72751, 208731, 231730, 273554, 279748, 422298, 1821146, 2439961, 2655408, 2748048, 3022960, 3174338, 4582596, 5001307, 6350113, 9137740, 11650986

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Example

The continued fraction for S(5)=1+1/8+1/1784+1/2322+1/2781 is {1, 7, 1, 10, 1, 2, 3, 1, 125, 1, 1, 6} where the largest element is 125=5^3 and 2781 is the smallest integer > 2322 with this property.

Mathematica

a[1] = 1; a[n_] := a[n] = Block[{s = Sum[1/a[i], {i, 1, n - 1}], k = a[n - 1] + 1}, While[ Max[ ContinuedFraction[s + 1/k]] != n^3, k++ ]; k]; Do[ Print[ a[n]], {n, 1, 28}]

Prog

(PARI) s=1; t=1; for(n=2, 17, s=s+1/t; while(abs(n^3-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))

Crossrefs

Sequence in context: A050642 A050648 A292695 * A159386 A160302 A002672

Adjacent sequences: A070900 A070901 A070902 * A070904 A070905 A070906

Keyword

easy,nonn

Author

Benoit Cloitre, May 19 2002

Extensions

Edited and extended by Robert G. Wilson v, Jun 10 2002

Status

approved