A097952 Sum of the number of digits in the prime numbers less than 10^n.

0, 4, 46, 475, 4719, 46534, 459970, 4562537, 45337545, 451112256, 4493162026, 44786187348, 446664473808, 4456613596481, 44480880591963, 444075310669968, 4434375640450064, 44287795522995300, 442382943864554586

Offset: 0

Author

Cino Hilliard, Sep 05 2004

Keywords

• nonn
• base

Comments

Partial sums of A046719(n) = n*A006879(n). In other words, a(n) is the number of digits used in writing out all {A006880(n)} primes below 10^n. - Lekraj Beedassy, Dec 13 2007

Examples

			There are 25 primes < 100; 4 of them are 1-digit numbers and 21 are 2-digit numbers. Thus a(2) = 4 + 21*2 = 46.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..28

Crossrefs

Cf. A006879, A006880, A046719, A119290.

Programs

Mathematica

Accumulate[Table[n(PrimePi[10^n]-PrimePi[10^(n-1)]),{n,0,14}]] (* This generates the first 15 terms of the sequence, but if n exceeds 14 the function PrimePi in Mathematica cannot calculate it. *) (* Harvey P. Dale, Jun 13 2014 *)

PARI

g(n) = for(j=0,n,s=0;forprime(x=2,10^j,y=length(Str(x));s+=y);print1(s","))

Formula

a(n) = Sum_{k=0..n} k * A006879(k). - Amiram Eldar, Jul 04 2024

Extensions

More terms derived from A006879 by R. J. Mathar, Oct 14 2010