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A075829 Let u(1)=x, u(n+1)=(n^2/u(n))+1; then u(n)=(b(n)*x+c(n))/(d(n)*x+a(n)). 5
1, 0, 1, 1, 5, 13, 23, 101, 307, 641, 893, 7303, 9613, 97249, 122989, 19793, 48595, 681971, 818107, 13093585, 77107553, 66022193, 76603673, 1529091919, 1752184789, 7690078169, 8719737569, 23184641107, 3721854001, 96460418429 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

for x real >0 lim n -> infinity abs(u(n)-n) = (x-1)/(1+(x-1)*log(2)).

Difference between denominator and numerator of the (n-1)-th alternating harmonic number Sum[(-1)^(k+1)*1/k,{k,1,n-1}] = A058313(n-1)/A058312(n-1). - Alexander Adamchuk, Jul 22 2006

LINKS

Table of n, a(n) for n=1..30.

FORMULA

a(n)=A024168(n-1)/gcd(A024168(n-1), A024168(n)). - Michael Somos, Oct 29, 2002

a(n) = A058312(n-1) - A058313(n-1) for n>1; a(1)=1. a(n) = Denominator[Sum[(-1)^(k+1)*1/k,{k,1,n-1}]] - Numerator[Sum[(-1)^(k+1)*1/k,{k,1,n-1}]]. - Alexander Adamchuk, Jul 22 2006

MATHEMATICA

Denominator[Table[Sum[(-1)^(k+1)*1/k, {k, 1, n-1}], {n, 1, 30}]]-Numerator[Table[Sum[(-1)^(k+1)*1/k, {k, 1, n-1}], {n, 1, 30}]] - Alexander Adamchuk, Jul 22 2006

PROG

(PARI) u(n)=if(n<2, x, (n-1)^2/u(n-1)+1); a(n)=polcoeff(denominator(u(n)), 0, x)

CROSSREFS

Cf. A075827, A075828, A075830.

Cf. A058312, A058313.

Sequence in context: A213483 A049833 A083800 * A119248 A114998 A140090

Adjacent sequences:  A075826 A075827 A075828 * A075830 A075831 A075832

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Oct 14 2002

STATUS

approved

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Last modified April 24 00:02 EDT 2019. Contains 322404 sequences. (Running on oeis4.)