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Search: id:A099260
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| A099260 |
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Number of decimal digits in (10^n)-th prime number. |
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+0
2
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| 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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).
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EXAMPLE
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a(4) = 6 because A006988(4) = prime(10^4) = 104729 has six decimal digits.
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CROSSREFS
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Cf. A006988 ((10^n)-th prime), A006880 (pi(10^n)), A099261 (bit lengths).
Sequence in context: A071789 A131870 A004724 this_sequence A053241 A132329 A052413
Adjacent sequences: A099257 A099258 A099259 this_sequence A099261 A099262 A099263
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KEYWORD
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more,nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Oct 10 2004
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