A070899 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 3n.

1, 6, 13, 16, 49, 71, 124, 188, 298, 326, 333, 354, 440, 797, 832, 954, 1006, 1040, 1280, 1319, 1414, 2038, 2113, 2231, 2291, 2924, 2973, 3107, 3983, 3984, 4331, 4605, 4763, 5756, 6314, 6325, 6402, 7501, 7967, 8073, 8143, 8895, 9567, 9900, 10333

Offset

1,2

Comments

sum(k=>1,1/a(k))=C=1.3...

Links

Table of n, a(n) for n=1..45.

Example

The continued fraction for S(7)=1+1/6+1/13+1/16+1/49+1/71+1/124 is [1, 2, 1, 6, 1, 1, 2, 3, 3, 1, 21, 1, 1, 3, 1, 3, 18, 3] where the largest element is 21=3*7 and 124 is the smallest integer > a(6)=71 with this property, hence a(7)=124.

Prog

(PARI) s=1; t=1; for(n=1, 60, s=s+1/t; while(abs(3*n-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))

Crossrefs

Sequence in context: A053753 A228380 A090068 * A265756 A332988 A333011

Adjacent sequences: A070896 A070897 A070898 * A070900 A070901 A070902

Keyword

easy,nonn

Author

Benoit Cloitre, May 19 2002

Status

approved