A071013 a(0)=1, a(n) is the smallest number > a(n-1) such that the simple continued fraction for S(n)=1/a(0)+1/a(1)+...+1/a(n) contains exactly 2n elements.

1, 2, 5, 7, 12, 25, 119, 152, 154, 163, 164, 178, 179, 183, 190, 192, 245, 267, 279, 290, 306, 313, 359, 420, 454, 496, 528, 576, 592, 615, 649, 661, 674, 702, 760, 830, 868, 945, 967, 978, 1000, 1167, 1190, 1194, 1209, 1288, 1289, 1325, 1452, 1892, 2084

Offset

0,2

Links

Table of n, a(n) for n=0..50.

Example

The simple continued fraction for S(4)=1+1/2+1/5+1/7+1/12 is [1, 1, 12, 1, 1, 4, 1, 2] which contains exactly 8 elements. The simple continued fraction for 1+1/2+1/5+1/7+1/12+1/25 is [1, 1, 28, 1, 1, 2, 1, 2, 1, 2] which contains exactly 10=2*5 elements and 25 is the smallest integer>12 with this property, hence a(5)=25.

Prog

(PARI) s=1; t=1; for(n=1, 78, s=s+1/t; while(abs(2*n-length(contfrac(s+1/t)))>0, t++); print1(t, ", "))

Crossrefs

Sequence in context: A213044 A269769 A230428 * A114727 A295334 A041033

Adjacent sequences: A071010 A071011 A071012 * A071014 A071015 A071016

Keyword

easy,nonn

Author

Benoit Cloitre, May 19 2002

Status

approved