A068160 Smallest prime beginning and ending in exactly n 1's and containing at least one digit != 1.

2, 101, 11311, 1114111, 111181111, 111110611111, 1111118111111, 111111151111111, 111111110911111111, 11111111128111111111, 111111111161111111111, 111111111110911111111111, 11111111111104111111111111, 1111111111111031111111111111, 11111111111111611111111111111, 11111111111111173111111111111111

Offset

0,1

Comments

a(499) has 1001 digits. - Michael S. Branicky, Oct 02 2024

Links

Michael S. Branicky, Table of n, a(n) for n = 0..498

Example

a(2) = 11311 is a prime that starts with 11 and ends in 11 (two 1's).

Prog

(Python)
from gmpy2 import is_prime
def a(n):
    suffix, d = (10**n-1)//9, 2*n+1
    while True:
        prefix = 10**(d-n)*suffix
        for mid in range(0, 10**(d-n), 10**n):
            s = str(mid//10**n)
            if s[0] == "1" or s[-1] == "1": continue
            t = prefix + mid + suffix
            if is_prime(t): return t
        d += 1
print([a(n) for n in range(16)]) # Michael S. Branicky, Oct 02 2024

Crossrefs

Cf. A366416.

Sequence in context: A266457 A028989 A113575 * A173640 A111012 A256516

Adjacent sequences: A068157 A068158 A068159 * A068161 A068162 A068163

Keyword

nonn,base

Author

Amarnath Murthy, Feb 24 2002

Extensions

Corrected and extended by Sascha Kurz, Jan 03 2003

More precise name and more terms from Hugo Pfoertner, Oct 11 2023

a(0) = 2 inserted by Michael S. Branicky, Oct 02 2024

Status

approved