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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A167543

Adjacent sequences:  A070895 A070896 A070897 * A070899 A070900 A070901

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 19 2002

STATUS

approved

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Last modified May 8 21:32 EDT 2021. Contains 343668 sequences. (Running on oeis4.)