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

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Last modified June 26 12:28 EDT 2022. Contains 354882 sequences. (Running on oeis4.)