A069588 Smallest prime in which the n-th significant digit is a 1.

11, 11, 101, 1009, 10007, 100003, 1000003, 10000019, 100000007, 1000000007, 10000000019, 100000000003, 1000000000039, 10000000000037, 100000000000031, 1000000000000037, 10000000000000061, 100000000000000003, 1000000000000000003, 10000000000000000051

Offset: 1

Author

Amarnath Murthy, Mar 25 2002

Keywords

• nonn
• base

Comments

Essentially (i.e., except for the initial term), the same as A003617. The definition is misleading, since "n-th significant digit" seems to mean here "most significant digit" (except for a(1)), while the "significance" is decreasing when going from the first to the last digit. (E.g., 1234 rounded to 2 significant digits is 1200, so "1,2" should be the first and second (and not fourth and third) significant digits.) [M. F. Hasler, Jun 03 2009]

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1000

Programs

Maple

11,seq(nextprime(10^j),j=1..30);

Mathematica

Join[{11}, NextPrime[10^Range[20]]] (* Paolo Xausa, Jun 23 2024 *)

Python

from sympy import nextprime
def a(n): return 11 if n == 1 else nextprime(10**(n-1))
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Nov 11 2021

Extensions

More terms from Sascha Kurz, Mar 28 2002

a(19) and beyond from Michael S. Branicky, Nov 11 2021