

A071012


a(1)=1, a(n) is the smallest number > a(n1) such that the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) contains exactly n elements.


1



1, 2, 3, 11, 16, 21, 27, 35, 42, 51, 55, 63, 75, 89, 350, 364, 385, 385, 416, 450, 453, 468, 476, 483, 526, 604, 617, 780, 1125, 1157, 1263, 1935, 7000, 7028, 7774, 8928, 9378, 62628, 865117
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..39.


EXAMPLE

The continued fraction for S(6)=1+1/2+1/3+1/11+1/16+1/21 is [2, 29, 9, 1, 3, 3] which contains 6 elements. The continued fraction for 1+1/2+1/3+1/11+1/16+1/21+1/27 is [2, 14, 169, 1, 1, 1, 4] which contains 7 elements and 27 is the smallest number >21 with this property, hence a(7)=27.


PROG

(PARI) s=1; t=1; for(n=1, 38, s=s+1/t; while(abs(nlength(contfrac(s+1/t)))>0, t++); print1(t, ", "))


CROSSREFS

Sequence in context: A144979 A194558 A076514 * A228520 A280969 A091734
Adjacent sequences: A071009 A071010 A071011 * A071013 A071014 A071015


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, May 19 2002


EXTENSIONS

One more term from Thomas Baruchel, Nov 16 2003


STATUS

approved



