A099260 -id:A099260 - cp's OEIS frontend

A006988 a(n) = (10^n)-th prime.

2, 29, 541, 7919, 104729, 1299709, 15485863, 179424673, 2038074743, 22801763489, 252097800623, 2760727302517, 29996224275833, 323780508946331, 3475385758524527, 37124508045065437, 394906913903735329, 4185296581467695669, 44211790234832169331

Offset: 0

N. J. A. Sloane, Robert G. Wilson v

Check the b-file for terms beyond those listed above.

			a(0) = 10^0-th prime = first prime = 2.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 111.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Marc Deleglise et al., Table of n, a(n) for n = 0..24 (a(23) corrected and a(24) added using Kim Walisch's primecount program, by David Baugh, Nov 11 2015)
C. K. Caldwell, Marc Deleglise's work on new values of pi(x)
UTM, The Nth Prime Page.
Eric Weisstein's World of Mathematics, Prime Number
R. G. Wilson, V, Letter to N. J. A. Sloane, Jan. 1989

Cf. A006880, A033844, A119780.

Cf. A099260, A274767 ((leading) digits of 103-digit a(100)).

A006988:=n->ithprime(10^n): seq(A006988(n), n=0..7); # Wesley Ivan Hurt, Nov 21 2014

Mathematica
```
Table[Prime[10^n], {n, 0, 12}]
```

a(n)=prime(10^n) \\ Charles R Greathouse IV, Jul 21 2011

More terms from Paul Zimmermann
a(19) from Marc Deleglise, Jun 29 2008
a(20) found by Andrey V. Kulsha using a program by Xavier Gourdon, Oct 05 2011
a(21) from Henri Lifchitz, Sep 09 2014
a(22) from Henri Lifchitz, Nov 21 2014

A099261 Length in bits of (10^n)-th prime number.

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Oct 11 2004

			a(1) = 5 because A006988(1) = prime(10^1) = 29 = 11101 (base 2) has five bits.

Pierre Dusart, Estimates of Some Functions Over Primes Without R.H.

Cf. A006988 ((10^n)-th prime), A006880 (pi(10^n)), A007053 (pi(2^n)), A099260 (decimal digit lengths).

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")"))

Extension, program, and reference from Charles R Greathouse IV, Aug 03 2010

cp's OEIS Frontend

A006988 a(n) = (10^n)-th prime.

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