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A217687 Values of n such that Fibonacci(n) gets increasingly closer to the powers of 10 (measured by the ratio between the Fibonacci number and the nearest power of 10). 1
1, 2, 6, 11, 16, 83, 150, 217, 662, 1107, 2954, 346893, 690832, 1034771, 1378710, 1722649, 2066588, 2410527, 2754466, 3098405, 3442344, 3786283, 4130222, 4474161, 4818100, 5162039, 5505978, 5849917, 6193856, 6537795, 6881734, 7225673, 7569612, 7913551, 8257490, 8601429, 8945368, 9289307, 9633246, 9977185 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sequence A217686 gives the sequence of values n such that Lucas(n) get increasingly closer to the powers of 10 (by the ratio between the Lucas number to the nearest power of 10).

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 A217686.

LINKS

Table of n, a(n) for n=0..39.

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(n), m++))

CROSSREFS

Cf. A217684, A217685, A217686, A217688.

Sequence in context: A193910 A215918 A078476 * A212459 A099056 A347315

Adjacent sequences:  A217684 A217685 A217686 * A217688 A217689 A217690

KEYWORD

nonn,base

AUTHOR

V. Raman, Oct 11 2012

STATUS

approved

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Last modified October 27 06:31 EDT 2021. Contains 348271 sequences. (Running on oeis4.)