A109677 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 3^n.

1, 9, 156, 1696, 3974, 21558, 82512, 631294, 5619414, 93118405, 739310894

Offset

1,2

Links

Table of n, a(n) for n=1..11.

Example

The continued fraction for S(5) = 1 + 1/9 + 1/156 + 1/1696 + 1/3974 is [1, 8, 2, 4, 2, 1, 2, 1, 5, 4, 1, 3, 2, 243, 1, 1, 3] where the largest element is 243=3^5 and 3974 is the smallest integer >1696 with this property.

Mathematica

a[1] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 1, s = Plus @@ (1/Table[a[i], {i, n - 1}])}, While[Log[3, Max[ContinuedFraction[s + 1/k]]] != n, k++ ]; k]; Do[ Print[ a[n]], {n, 11}] (* Robert G. Wilson v, Aug 08 2005 *)

Prog

(PARI) s=1; t=1; for(n=2, 50, s=s+1/t; while(abs(3^n-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))

Crossrefs

Sequence in context: A305139 A208545 A183471 * A320290 A024122 A230180

Adjacent sequences: A109674 A109675 A109676 * A109678 A109679 A109680

Keyword

hard,nonn

Author

Ryan Propper, Aug 06 2005

Status

approved