A064490 Smallest prime with prime(n) decimal digits.

11, 101, 10007, 1000003, 10000000019, 1000000000039, 10000000000000061, 1000000000000000003, 10000000000000000000009, 10000000000000000000000000331, 1000000000000000000000000000057, 1000000000000000000000000000000000067, 10000000000000000000000000000000000000121

Offset: 1

Author

Jason Earls, Oct 04 2001

Keywords

• base
• nonn

Examples

			11 is the first prime with 2 decimal digits.
101 is the first prime with 3 decimal digits.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..168 (first 75 terms from Harry J. Smith)

Crossrefs

Cf. A000040, A003617, A064489.

Programs

Maple

for n from 1 to 20 do p := ithprime(n): for i from 10^(p-1) to 10^p do if isprime(i) then printf(`%d,`,i); break; fi: od: od:
# second Maple program:
a:= n-> nextprime(10^(ithprime(n)-1)):
seq(a(n), n=1..15);  # Alois P. Heinz, Jun 24 2018

Mathematica

Table[NextPrime[10^(n-1)],{n,Prime[Range[15]]}] (* Harvey P. Dale, Feb 06 2020 *)

PARI

l(n)=ln=0; while(n,n=floor(n/10); ln++); return(ln);
a=0; for(n=1,10^6,x=l(prime(n)); if(isprime(x),b=x; if(b>a,a=b; print(prime(n)))))

PARI

{ for (n=1, 75, p=prime(n); a=nextprime(10^(p - 1)); write("b064490.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 16 2009

Python

from sympy import prime, nextprime, primepi
def a(n): return nextprime(10**(prime(n)-1))
print([a(n) for n in range(1, 14)]) # Michael S. Branicky, May 26 2021

Formula

a(n) = A003617(A000040(n)).

a(n) = A000040(A064489(n)).

Extensions

More terms from James Sellers, Oct 08 2001

Offset changed from 0 to 1 by Harry J. Smith, Sep 16 2009