A070901 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 prime(n).

1, 3, 8, 85, 103, 349, 361, 429, 500, 505, 1832, 1895, 1996, 2195, 2202, 2290, 2531, 2575, 2688, 3040, 3189, 3280, 3792, 5103, 5151, 7712, 21398, 21914, 22472, 22603, 22814, 23184, 23375, 24368, 24370, 24545, 24812, 25015, 25262, 25613, 26171

Offset

1,2

Comments

Sum(k=>1,1/a(k))=C=1.498...

Links

Table of n, a(n) for n=1..41.

Example

The continued fraction for S(4)=1+1/3+1/8+1/85 is [1, 2, 7, 1, 6, 5, 1, 2] where the largest element is 7=prime(4).

Prog

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

Crossrefs

Sequence in context: A233175 A347920 A367273 * A079657 A136309 A266671

Adjacent sequences: A070898 A070899 A070900 * A070902 A070903 A070904

Keyword

easy,nonn

Author

Benoit Cloitre, May 19 2002

Status

approved