

A008963


Initial digit of Fibonacci number F(n).


24



0, 1, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 6, 9, 1, 2, 4, 6, 1, 1, 2, 4, 7, 1, 1, 3, 5, 8, 1, 2, 3, 5, 9, 1, 2, 3, 6, 1, 1, 2, 4, 7, 1, 1, 2, 4, 7, 1, 2, 3, 5, 8, 1, 2, 3, 5, 9, 1, 2, 4, 6, 1, 1, 2, 4, 7, 1, 1, 3, 4, 8, 1, 2, 3, 5, 8, 1, 2, 3, 6, 9, 1, 2, 4, 6, 1, 1, 2, 4, 7, 1, 1, 3, 5, 8, 1
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OFFSET

0,4


COMMENTS

Benford's law applies since the Fibonacci sequence is of exponential growth: P(d)=log_10(1+1/d), in fact among first 5000 values the digit d=1 appears 1505 times, while 5000*P(1) is about 1505.15.  Carmine Suriano, Feb 14 2011
Wlodarski observed and Webb proved that the distribution of terms of this sequence follows Benford's law.  Amiram Eldar, Sep 23 2019


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000
William Webb, Distribution of the first digits of Fibonacci numbers, The Fibonacci Quarterly, Vol. 13, No. 4 (1975), pp. 334336.
Wikipedia, Benford's law
J. Wlodarski, Fibonacci and Lucas Numbers Tend to Obey Benford's Law, The Fibonacci Quarterly, Vol. 9, No. 1 (1971), pp. 8788.
Index entries for sequences related to Benford's law


FORMULA

a(n) = A000030(A000045(n)).  Amiram Eldar, Sep 23 2019


MATHEMATICA

Table[IntegerDigits[Fibonacci[n]][[1]], {n, 0, 100}] (* T. D. Noe, Sep 23 2011 *)


PROG

(PARI) vector(10001, n, f=fibonacci(n1); f\10^(#Str(f)1))
(Haskell)
a008963 = a000030 . a000045  Reinhard Zumkeller, Sep 09 2015


CROSSREFS

Cf. A000045, A003893 (final digit).
Cf. A000030, A261607, A213201.
Sequence in context: A105994 A120496 A105150 * A031324 A226251 A093086
Adjacent sequences: A008960 A008961 A008962 * A008964 A008965 A008966


KEYWORD

nonn,base,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



