A070902 - OEIS

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A070902

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 n^2.

1, 4, 14, 19, 25, 282, 393, 415, 460, 501, 1839, 2835, 3422, 4718, 4909, 6350, 6678, 11087, 12941, 16503, 16568, 21585, 24446, 31506, 35164, 35380, 40323, 46001, 46905, 52205, 56210, 56441, 60038, 92562, 97354, 101710, 102136, 107680, 127299

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OFFSET

1,2

COMMENTS

sum(k=>1,1/a(k))=C=1.429...

LINKS

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

EXAMPLE

The continued fraction for S(6)=1+1/4+1/14+1/19+1/25+1/282 is [1, 2, 2, 1, 1, 6, 1, 4, 5, 36, 1, 3, 2, 2] where the largest element is 36=6^2 and 282 is the smallest integer > 25 with this property.

PROG

(PARI) s=1; t=1; for(n=2, 47, s=s+1/t; while(abs(n^2-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))

CROSSREFS

Sequence in context: A336634 A045248 A271375 * A059007 A035401 A139330

Adjacent sequences: A070899 A070900 A070901 * A070903 A070904 A070905

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 19 2002

STATUS

approved