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A099261
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Length in bits of (10^n)-th prime number.
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1
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2, 5, 10, 13, 17, 21, 24, 28, 31, 35, 38, 42, 45, 49, 52, 56, 59, 62, 66, 69, 73, 76, 79, 83, 86, 89, 93, 96, 100, 103, 106, 110, 113, 116, 120, 123, 127, 130, 133, 137, 140, 143, 147, 150, 153, 157, 160, 163, 167, 170, 173, 177, 180, 184, 187, 190, 194, 197, 200, 204
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Pierre Dusart, Estimates of Some Functions Over Primes Without R.H.
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EXAMPLE
| a(1) = 5 because A006988(1) = prime(10^1) = 29 = 11101 (base 2) has five bits.
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PROG
| (PARI) a(n)=if(n<3, return([2, 5, 10][n+1])); my(l=n*log(10), ll=log(l), x=n*log(10)/log(2), lb=ceil(x+log(l+ll-1+(ll-2.2)/l)/log(2)), ub=ceil(x+log(l+ll-1+(ll-2)/l)/log(2))); if(lb==ub, lb, error("Cannot determine a("n")"))
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CROSSREFS
| Cf. A006988 ((10^n)-th prime), A006880 (pi(10^n)), A007053 (pi(2^n)), A099260 (decimal digit lengths).
Sequence in context: A188025 A187949 A180161 * A103215 A037942 A008784
Adjacent sequences: A099258 A099259 A099260 * A099262 A099263 A099264
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KEYWORD
| nonn,base
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Oct 11 2004
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EXTENSIONS
| Extension, program, and reference from Charles R Greathouse IV (charles.greathouse(AT)case.edu), Aug 03 2010
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