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A308945 Number of totient numbers, phi(k), k <= 10^n, whose initial digit is 1. 0

%I

%S 2,20,213,2152,21594,216009,2159776,21595522,215951111,2159507603,

%T 21595061256,215950604593

%N Number of totient numbers, phi(k), k <= 10^n, whose initial digit is 1.

%C The probability that a totient number starts with an initial 1 does not obey Benford's law however it does appear to tend to a constant value. In a sample of 10^9 totient numbers the distribution of initial digits 1 - 9 is approx. 21.595%, 20.774%, 16.457%, 12.682%, 7.904%, 6.633%, 5.505%, 4.634%, 3.816%.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Benford%27s_law">Benford's law</a>

%e a(1)=2 as the first 10 totient numbers are {1, 1, 2, 2, 4, 2, 6, 4, 6, 4} and the occurrence of numbers with an initial 1 is 2.

%t lst1={}; Do[lst=Table[0, {n, 1, 9}]; Do[++lst[[First@IntegerDigits@EulerPhi[n]]], {n, 1, 10^m}]; AppendTo[lst1, lst[[1]]], {m, 1, 7}]; lst1

%o (PARI) a(n) = {k=0; for(j=1, 10^n, if(digits(eulerphi(j))[1]==1, k++)); k} \\ _Jinyuan Wang_, Jul 04 2019

%Y Cf. A000010, A047855, A073517, A073557.

%K nonn,base,more

%O 1,1

%A _Frank M Jackson_, Jul 02 2019

%E a(10)-a(12) from _Giovanni Resta_, Jul 04 2019

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Last modified June 20 06:56 EDT 2021. Contains 345157 sequences. (Running on oeis4.)