A070898 a(0)=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(0)+1/a(1)+1/a(2)+...+1/a(n) equals 2n.

1, 2, 7, 15, 16, 23, 50, 60, 72, 123, 149, 164, 166, 185, 236, 494, 495, 569, 589, 654, 802, 951, 968, 1068, 1178, 1323, 1356, 1379, 1399, 1487, 1946, 2458, 2500, 2786, 2911, 3077, 4282, 4916, 5156, 5591, 6047, 6103, 6639, 7095, 7786, 8068, 8493, 9456

Offset

0,2

Comments

sum(k=>1,1/a(k))=C=1.9...

Links

Table of n, a(n) for n=0..47.

Example

The simple continued fraction for S(3)=1/a(0)+1/a(1)+1/a(2)+1/a(3)=1+1/2+1/7+1/15 is [1, 1, 2, 2, 3, 1, 6] where the largest element is 6=2*3. The simple continued fraction for 1+1/2+1/7+1/15+1/16 is [1, 1, 3, 2, 1, 1, 2, 2, 1, 8] where 8=2*4 is the largest element. Hence a(4)=16.

Prog

(PARI) s=1; t=1; for(n=1, 60, s=s+1/t; while(abs(2*n-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))

Crossrefs

Sequence in context: A132997 A088824 A034903 * A132746 A252475 A350043

Adjacent sequences: A070895 A070896 A070897 * A070899 A070900 A070901

Keyword

easy,nonn

Author

Benoit Cloitre, May 19 2002

Status

approved