A064489 a(n) is the smallest number m such that prime(m) has prime(n) decimal digits.

5, 26, 1230, 78499, 455052512, 37607912019, 279238341033926, 24739954287740861, 201467286689315906291, 157589269275973410412739599

Offset: 1

Author

Jason Earls, Oct 04 2001

Keywords

• base
• nonn
• hard
• more

Examples

			For n = 1: a(1) = 5 because prime(5) = 11 is the first prime with 2 = prime(1) decimal digits.
		

Crossrefs

Cf. A000040, A000720, A006880, A064490.

Programs

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; print1(n, ", "))))

Python

from sympy import prime, nextprime, primepi
def a(n): return primepi(nextprime(10**(prime(n)-1)))
print([a(n) for n in range(1, 6)]) # Michael S. Branicky, May 26 2021

Formula

a(n) = 1 + A006880(A000040(n)-1). [Corrected by Amiram Eldar, Sep 03 2024]

a(n) = A000720(A064490(n)).

Extensions

More terms from David Wasserman, Jul 22 2002

a(10) from the b-file at A006880 added by Amiram Eldar, Sep 03 2024