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

1,1

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)

Formula

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

Prog

(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

Crossrefs

Cf. A069100.

Sequence in context: A002863 A047693 A212265 * A323230 A393926 A392965

Adjacent sequences: A107105 A107106 A107107 * A107109 A107110 A107111

Keyword

nonn,base

Author

Zak Seidov, May 12 2005

Extensions

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

More terms from David A. Corneth, Jun 16 2021

Status

approved