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A217688 Values of n such that 10^n gets increasingly closer to a Fibonacci number (measured by the ratio between the power of 10 and the nearest Fibonacci number). 1
0, 1, 2, 3, 17, 31, 45, 138, 231, 617, 72496, 144375, 216254, 288133, 360012, 431891, 503770, 575649, 647528, 719407, 791286, 863165, 935044, 1006923, 1078802, 1150681, 1222560, 1294439, 1366318, 1438197, 1510076, 1581955, 1653834, 1725713, 1797592, 1869471, 1941350, 2013229, 2085108, 2156987 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The sequence A217685 gives the sequence of values n such that 10^n gets increasingly closer to a Lucas number.

Given that for sufficiently large values of n, Fibonacci(n) ~ Lucas(n)/sqrt(5) ~ (((1+sqrt(5))/2)^n)/(sqrt(5)), the intermediate differences between the terms in this sequence also need to be a member of the sequence A217685.

LINKS

Table of n, a(n) for n=1..40.

PROG

(PARI) default(realprecision, 1000); a=vector(100, i, (contfracpnqn(contfrac(log((1+sqrt(5))/2)/log(10), 0, i))[2, 1]))

log_fibonacci(j)=(j*log((1+sqrt(5))/2)/log(10))-(log(sqrt(5))/log(10))

deviation(k)=abs(round(log_fibonacci(k))-log_fibonacci(k))

n=6; err=deviation(n); m=3; while(n<10^20, if(deviation(n+a[m])<err, n=n+a[m]; err=deviation(n); print(round(log_fibonacci(n))), m++))

CROSSREFS

Cf. A217684, A217685, A217686, A217687.

Sequence in context: A215280 A219559 A193051 * A263570 A029733 A153686

Adjacent sequences:  A217685 A217686 A217687 * A217689 A217690 A217691

KEYWORD

nonn,base

AUTHOR

V. Raman, Oct 11 2012

STATUS

approved

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Last modified October 21 11:09 EDT 2021. Contains 348150 sequences. (Running on oeis4.)