# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a141053
Showing 1-1 of 1

%I A141053 #30 Feb 11 2024 23:44:58
%S A141053 2,2,2,2,2,3,3,3,4,4,5,5,6,7,8,8,9,1,1,1,1,1,1,2,2,2,2,3,3,3,4,4,5,5,
%T A141053 6,7,7,8,9,1,1,1,1,1,1,1,2,2,2,3,3,3,4,4,5,5,6,6,7,8,9,1,1,1,1,1,1,1,
%U A141053 2,2,2
%N A141053 Most-significant decimal digit of Fibonacci(5n+3).
%C A141053 Leading digit of A134490(n).
%C A141053 From _Johannes W. Meijer_, Jul 06 2011: (Start)
%C A141053 The leading digit d, 1 <= d <= 9, of A141053 follows Benford’s Law. This law states that the probability for the leading digit is p(d) = log_10(1+1/d), see the examples.
%C A141053 We observe that the last digit of A134490(n), i.e. F(5*n+3) mod 10, leads to the Lucas sequence A000032(n) (mod 10), i.e. a repetitive sequence of 12 digits [2, 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9] with p(0) = p(5) = 0, p(1) = p(3) = p(7) = p(9) = 1/6 and p(2) = p(4) = p(6) = p(8) = 1/12. This does not obey Benford’s Law, which would predict that the last digit would satisfy p(d) = 1/10, see the links. (End)
%H A141053 Kevin Brown, <a href="http://www.mathpages.com/home/kmath302/kmath302.htm">Benford's Law</a>.
%H A141053 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BenfordsLaw.html">Benford's Law</a>.
%H A141053 Wikipedia, <a href="http://en.wikipedia.org/wiki/Benford&#39;s_law">Benford's Law</a>.
%H A141053 <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>
%F A141053 a(n) = floor(F(5*n+3)/10^(floor(log(F(5*n+3))/log(10)))). - _Johannes W. Meijer_, Jul 06 2011
%e A141053 From _Johannes W. Meijer_, Jul 06 2011: (Start)
%e A141053 d     p(N=2000) p(N=4000) p(N=6000) p(Benford)
%e A141053 1      0.29900   0.29950   0.30033   0.30103
%e A141053 2      0.17700   0.17675   0.17650   0.17609
%e A141053 3      0.12550   0.12525   0.12517   0.12494
%e A141053 4      0.09650   0.09675   0.09700   0.09691
%e A141053 5      0.07950   0.07950   0.07933   0.07918
%e A141053 6      0.06700   0.06675   0.06700   0.06695
%e A141053 7      0.05800   0.05825   0.05800   0.05799
%e A141053 8      0.05150   0.05125   0.05100   0.05115
%e A141053 9      0.04600   0.04600   0.04567   0.04576
%e A141053 Total  1.00000   1.00000   1.00000   1.00000 (End)
%p A141053 A134490 := proc(n) combinat[fibonacci](5*n+3) ; end proc:
%p A141053 A141053 := proc(n) convert(A134490(n),base,10) ; op(-1,%) ; end proc:
%p A141053 seq(A141053(n),n=0..70) ; # _R. J. Mathar_, Jul 04 2011
%Y A141053 Cf. A000045 (F(n)), A008963 (Initial digit F(n)), A105511-A105519, A003893 (F(n) mod 10), A130893, A186190 (First digit tribonacci), A008952 (Leading digit 2^n), A008905 (Leading digit n!), A045510, A112420 (Leading digit Collatz 3*n+1 starting with 1117065), A007524 (log_10(2)), A104140 (1-log_10(9)). - _Johannes W. Meijer_, Jul 06 2011
%K A141053 nonn,base,less
%O A141053 0,1
%A A141053 _Paul Curtz_, Aug 01 2008
%E A141053 Edited by _Johannes W. Meijer_, Jul 06 2011

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE