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

2, 20, 213, 2152, 21594, 216009, 2159776, 21595522, 215951111, 2159507603, 21595061256, 215950604593

Offset

1,1

Comments

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%.

Links

Table of n, a(n) for n=1..12.

Wikipedia, Benford's law

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A047855, A073517, A073557.

Sequence in context: A067636 A226301 A000906 * A356853 A199761 A214769

Adjacent sequences: A308942 A308943 A308944 * A308946 A308947 A308948

Keyword

nonn,base,more

Author

Frank M Jackson, Jul 02 2019

Extensions

a(10)-a(12) from Giovanni Resta, Jul 04 2019

Status

approved