A064490 Smallest prime with prime(n) decimal digits.

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

Offset

1,1

Links

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

Formula

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000040, A003617, A064489.

Sequence in context: A075767 A292014 A080176 * A080439 A098153 A020449

Adjacent sequences: A064487 A064488 A064489 * A064491 A064492 A064493

Keyword

base,nonn

Author

Jason Earls, Oct 04 2001

Extensions

More terms from James A. Sellers, Oct 08 2001

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

Status

approved