Search: id:A099260
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%I A099260
%S A099260 1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23
%N A099260 Number of decimal digits in (10^n)-th prime number.
%C A099260 Some terms have been deduced from A006880's terms. As lim {n->oo} p_n/
               (n logn) = 1 is equivalent to the prime number theorem (see, for 
               example, Elementary Introduction to Number Theory by Calvin T. Long, 
               1972, p. 67), a good first approximation (without having done any 
               detailed analysis) should be a(n)=floor(log_10((10^n)*log(10^n))), 
               which correctly generates all the first 22 terms and predicts that 
               the sequence will continue 24,25,...,43,44,46,47,...,435,436,438,
               439,...,4344,4345,4347,4348,...,4503,4504 through the first 4500 
               terms (with only 5,45,437,4346 not appearing - compare with the digits 
               of log_10(e) in A002285).
%e A099260 a(4) = 6 because A006988(4) = prime(10^4) = 104729 has six decimal digits.
%Y A099260 Cf. A006988 ((10^n)-th prime), A006880 (pi(10^n)), A099261 (bit lengths).
%Y A099260 Sequence in context: A071789 A131870 A004724 this_sequence A053241 A132329 
               A052413
%Y A099260 Adjacent sequences: A099257 A099258 A099259 this_sequence A099261 A099262 
               A099263
%K A099260 more,nonn
%O A099260 0,2
%A A099260 Rick L. Shepherd (rshepherd2(AT)hotmail.com), Oct 10 2004

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