A068160 - OEIS

%I #18 Oct 02 2024 12:18:36

%S 2,101,11311,1114111,111181111,111110611111,1111118111111,

%T 111111151111111,111111110911111111,11111111128111111111,

%U 111111111161111111111,111111111110911111111111,11111111111104111111111111,1111111111111031111111111111,11111111111111611111111111111,11111111111111173111111111111111

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

%C a(499) has 1001 digits. - _Michael S. Branicky_, Oct 02 2024

%H Michael S. Branicky, <a href="/A068160/b068160.txt">Table of n, a(n) for n = 0..498</a>

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

%o (Python)

%o from gmpy2 import is_prime

%o def a(n):

%o     suffix, d = (10**n-1)//9, 2*n+1

%o     while True:

%o         prefix = 10**(d-n)*suffix

%o         for mid in range(0, 10**(d-n), 10**n):

%o             s = str(mid//10**n)

%o             if s[0] == "1" or s[-1] == "1": continue

%o             t = prefix + mid + suffix

%o             if is_prime(t): return t

%o         d += 1

%o print([a(n) for n in range(16)]) # _Michael S. Branicky_, Oct 02 2024

%Y Cf. A366416.

%K nonn,base

%O 0,1

%A _Amarnath Murthy_, Feb 24 2002

%E Corrected and extended by _Sascha Kurz_, Jan 03 2003

%E More precise name and more terms from _Hugo Pfoertner_, Oct 11 2023

%E a(0) = 2 inserted by _Michael S. Branicky_, Oct 02 2024