OFFSET
1,6
COMMENTS
Considering the frequency of all decimal digits in leading position of prime numbers (A065681 - A065687), we cannot apply Benford's Law. But we observe at 10^e - levels that the frequency for 0 to 9 decreases monotonically, at least in the small range until 10^7.
The "begins with 9" sequence is too dull to include. - N. J. A. Sloane
Note that the primes do not satisfy Benford's law (see A000040). - N. J. A. Sloane, Feb 08 2017
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Benford's Law
EXAMPLE
MATHEMATICA
Accumulate[If[First[IntegerDigits[#]]==1, 1, 0]&/@Prime[Range[80]]] (* Harvey P. Dale, Jan 22 2013 *)
PROG
(PARI) digitsIn(x)= { local(d); if (x==0, return(1)); d=1 + log(x)\log(10); if (10^d == x, d++, if (10^(d-1) > x, d--)); return(d) } MSD(x)= { return(x\10^(digitsIn(x)-1)) } { a=0; p=2; for (n=1, 1000, q=prime(n); while (p <= q, if(MSD(p) == 1, a++); p=nextprime(p+1)); write("b065680.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 26 2009
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Reinhard Zumkeller, Nov 13 2001
STATUS
approved