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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
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
Sequence in context: A193910 A215918 A078476 * A212459 A099056 A347315
KEYWORD
nonn,base
AUTHOR
V. Raman, Oct 11 2012
STATUS
approved

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Last modified March 1 06:21 EST 2024. Contains 370430 sequences. (Running on oeis4.)