A107108 Shorthand of n-th smallest n-digit prime, see comments.

2, 3, 7, 21, 61, 69, 117, 189, 193, 181, 259, 193, 303, 411, 487, 513, 931, 591, 861, 667, 801, 1081, 711, 1027, 1321, 1753, 1581, 2109, 1527, 1951, 2613, 2053, 2533, 3171, 2653, 3073, 2769, 2899, 3201, 3133, 4089, 2859, 4447, 5367, 3819, 4923, 5251, 5109, 5127, 6721

Offset: 1

Author

Zak Seidov, May 12 2005

Keywords

• nonn
• base

Comments

To shorthand the n-th - smallest n-digit prime it is convenient to subtract 10^(n-1) (n>1). Compare a(n) with A069100(n).

Links

• David A. Corneth, Table of n, a(n) for n = 1..1000 (using b-file from A069100)

Crossrefs

Cf. A069100.

Programs

PARI

a(n)=prime(primepi(10^(n-1))+n)-if(n==1,0,10^(n-1)) \\ Franklin T. Adams-Watters, Mar 07 2014

PARI

a(n) = {if(n == 1, return(2)); my(t = 0); forprime(p = 10^(n-1), 10^n, t++; if(t==n, return(p - 10^(n-1))))} \\ David A. Corneth, Jun 16 2021

Python

from sympy import nextprime
def a(n):  return nextprime(10**(n-1), ith=n) - 10**(n-1) * (n > 1)
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, Jun 16 2021

Formula

a(1)=2; at n>1 a(n)=prime(pi[10^(n-1)]+n)-10^(n-1)=A069100(n)-10^(n-1).

Extensions

a(3) corrected by Franklin T. Adams-Watters, Mar 07 2014

More terms from David A. Corneth, Jun 16 2021