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%I #22 Dec 23 2021 10:04:07
%S 0,4,46,475,4719,46534,459970,4562537,45337545,451112256,4493162026,
%T 44786187348,446664473808,4456613596481,44480880591963,
%U 444075310669968,4434375640450064,44287795522995300,442382943864554586
%N Sum of the number of digits in the prime numbers less than 10^n.
%C 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
%C 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 14 2007
%e 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.
%t 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 *)
%o (PARI) g(n) = for(j=0,n,s=0;forprime(x=2,10^j,y=length(Str(x));s+=y);print1(s","))
%Y Cf. A006879, A006880, A046719, A119290.
%K nonn,base
%O 0,2
%A _Cino Hilliard_, Sep 05 2004
%E More terms derived from A006879 by _R. J. Mathar_, Oct 14 2010
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